(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Light and Electromagnetism Project Physics Text and Handbook 4"

The Project Physics Course 



Text and Handbook 



4 



Light and Electromagnetism 




The Project Physics Course 



Text and Handbook 



UNIT 



4 



Light and Electromagnetism 



A Component of the 
Project Physics Course 




Published by 

HOLT, RINEHART and WINSTON, Inc. 

New York, Toronto 



Directors of Harvard Project Physics 

Gerald Holton. Department of Physics. Harvard 

University 
F. James Rutherford, Capuchino High School, 

San Bruno. California, and Harvard University 
Fletcher G. Watson. Harvard Graduate School 

of Education 



Acknowledgments, Text Section 

The authors and publisher have made e\ ery effort 
to trace the ownership of all selections found in 
this book and to make full acknowledgment for 
their use. Many of the selections are in public 
domain. 

Grateful acknowledgment is hereby made to the 
following authors, publishers, agents, and in- 
di\ iduals for use of their copyrighted material. 



Special Consultant to Project Physics 

.Andrew Ahlgren, Harvard Graduate School of 
Education 



A partial list of staff and consultants to Harvard 
Project Physics appears on page iv. 



This Text and Handbook. Unit 4, is one of the 
many instructional materials developed for the 
Project Physics Course. These materials include 
Texts. Handbooks. Teacher Resource Books. 
Readers. Programmed Instruction Booklets. Film 
Loops. Transparencies. 16mm films, and laboratory 
equipment. 



Copyright i; 1970. Project Physics 

All Rights Reserved 

SBN 0.3-084502-5 

12.34 039 98765432 

Project Physics is a registered trademark 



P. 2 Newton, Sir Isaac, Neiuton's Philosophij of 
Nature, ed.. H. S. Thayer. Haffner Publishing 
Co.. N.Y.. 1953. pp. 68-81. 

P. 5 Blackmore. Richard. Creation. A Pliilosophi- 
ciil Poem. Robert Johnson, p. 91. 
P. 14 Young. Thomas. Course oj Lectures oti Natu- 
rcil Philosophij and the Mecliauical Arts. Cox. 
Pp. 17-19 Newton. Sir Isaac. Neiaton's Philosophij 
of Nature, ed.. H. S. Thayer. Haffner Publishing 
Co., N.Y.. 1953. pp. 68-81. 
P. 19 Thomson. James. The Poetical Works of 
James Thomson. William Tegg and Co.. pp. 145-146 
and p. 10. 

P. 20 Goethe. J. W.. Goethe As A Scientist. Magnus. 
Rudolf, translated by Heinz Norden. Henry Schu- 
man. pp. 184-185. copyright 1949 by Heinz Norden. 
P. 24 Young. Thomas. Miscellaneous Works 
(London. 1855) Vol. I. p. 415. 
P. 24 Glover. Richard. "A Poem on Newton." 
A View of Sir Isuoc Neivton's Pliilosopltij. 
S. Palmer, p. 15. 

P. 26 Galilei. Galileo. Dialogues Concerning Two 
Neic Sciences, trans. Crew. H. and de Salvio. A., 
copyright 1952 by Dover Publications, pp. 42-43. 
P. 28 Savage. Richard. ""The Wanderer."' The 
Poetical Works of Richard Savage, ed. Tracy. 
Clarence. Cambridge University Press, pp. 147-148. 
Pp. 32-34 Gilbert. William. De Magnete. trans. 
.Mottelay. P. Fleury. copyright 1958 by Dover 
Publications, pp. 1-14 and p. 121. 
P. 51 von Guericke. Otto. Magie. Wm. F., .4 Source- 
hook in PInjsics. McGraw-Hill. 1935. p. 393. 
P. 54 Volta, Alessandro. On the Electricitg 
Excited hij the Mere Contact of Conducting 
Suhstances of Different Kinds. Philosophical 
Transactions of the Royal Society of London. 1800. 
p. 403. 

P. 63 Ampere. Andre-Marie. Whittaker. E. T.. /\ 
Historg of the Theories of Aether and Electricity. 
Harper & Brothers. N.Y., 1960. p. 84. 
P. 78 Faraday. .Michael. MacDonald. D.K.C.. 
Furadag. Maxwell & Keliin. Science Studies 
Series. Doubleday. Garden City. 1964. p. 11. 
P. 80 Faraday. .Michael. Faradag's Diarg. G. Bell 
& Sons, London. 1932. Vol. I. pp. 375-376. 



Much of the historical information in Chapter 15. 
in particular the discussion of the ac-dc contro- 
versy, is based on the book by Harold I. Sharlin. 
The Making of the Electrical .Age (Abelard- 
Schuman. New York. 1963). We are grateful to 
Professor Sharlin for giving his permission to 
use this material. 



p. 104 Maxwell, James Clerk. T/ie Scientific Papers 

of James Clerk Maxuell. ed.. Niven, W. D., Dover 

Publications, N.Y., 1965, p. 158. 

P. 110 Maxwell, James Clerk. The Scientific Papers 

of James Clerk Maxwell, ed., Niven, W. D., Dover 

Publications, N.Y., 1965. p. 500. 

P. 121 Maxwell, James Clerk, T/;e Scientific Papers 

of James Clerk Maxwell, ed., Niven, W. D.. Dover 

Publications, N.Y., 1965, p. 775 of Vol. II. 

P. 121 Maxwell, James Clerk, T/ze Scientific Papers 

of James Clerk Maxwell, ed., Niven, W. D.. Dover 

Publications. N.Y., 1965. p. 763 of Vol. II. 

P. 125 Carroll, Lewis. The Complete Works of Lewis 

Carroll. Random House. N.Y., 1939, pp. 66-67. 

Pp. 126-127 Feynman, R. P.. The Feijnman Lectures 

on Physics. Feynman. R. P.. Leighton. R. B.. and 

Sands, M.. Vol. 2. Addison-Wesley, 1964, pp. 9-10. 

Picture Credits, Text Section 

Cover photograph : from the book A History 
of Electricity by Edward Tatnall Canby, © by 
Eric Nitsche Int'I. Published by Hawthorn Books, 
Inc., 70 Fifth Avenue, New York, New York 

(Facing page 1) (top left) Euler, Leonhard, 
Theoria Motuiim Planetarum et Cometarum, 
Berlin, 1744; (bottom left) Descartes, Rene, 
Principia Philosophiae , 1664; (top right) 
Maxwell, James Clerk, A Treatise on Electricity 
and Magnetism, vol. II, Oxford Press, 1892. 

P. 3 National Radio Astronomy Observatory, 
Greenbank, West Virginia. 

Pp. 4, 5 "Grand Tetons & Snake River." 
Minor White. 

P. 7 (Delphi) Greek National Tourist Office; 
(plane) American Airlines; (light through prism) 
Bausch & Lomb Optical Co. 

P. 8 (camera obscura) Frisius, Reiner Gemma, 
De Radio Astronomico et Geometrico Liber, 1545. 

Pp. 1 1 , 12 Bausch & Lomb Optical Co. 

P. 13 (portrait) Engraved by G. R. Ward, from 
a picture by Sir Thomas Lawrence. 

P. 15 (portrait) Cabinet des Estampes 
Bibliotheque Nationale, Paris. 

Pp. 14, 16 (diffraction patterns) Cagnet, 
Francon & Thrierr, Atlas of Optical Phenomena, 
c 1962, Springer- Verlag OHG, Berlin. 

P. 16 (radio telescope) National Radio Astron- 
omy Observatory, Greenbank, West Virginia. 

P. 25 Courtesy of the Fogg Art Museum. Har- 
vard University. GrenviUe L. Winthrop bequest. 

P. 29 Reprinted by permission from F. W. Sears, 
Optics, 3rd Ed., 1949, Addison-Wesley, Reading, 
Mass. 

P. 30 Courtesy of the Lawrence Radiation 
Laboratory, University of California, Berkeley. 

P. 36 from a painting by Mason Chamberlain 
in 1762, engraved by C. Turner. Courtesy of 
Burndy Library. 

P. 38 (portrait) Musee de Versailles; (drawing) 
from Coulomb's memoire to the French Academy 
of Sciences, 1785. 

Pp. 48, 49 (all photographs) Courtesy of Mr. 
Harold M. Waage, Palmer Physical Laboratory, 
Princeton University. 

P. 53 The van Marum electrical machine, 1784. 
Courtesy of the Burndy Library. 



P. 54 (portrait) The Science Museum, London; 
(Franklin's drawing) American Academy of Arts 
and Sciences. 

P. 57 Courtesy of Stanford University. 

P. 61 (portrait) Nationalhistoriske Museum, 
Frederiksborg; (bottom left) from PSSC Physics, 
D. C. Heath and Company, Boston, 1965. 

P. 62 (field photo) from Photographs of Physi- 
cal Phenomena, c Kodansha, Tokyo, 1968; 
(portrait) Bibliotheque de I'Academie des Sciences. 

P. 63 (model) Crown copyright. Science 
Museum, London. 

P. 64 (bottom photograph) General Electric 
Research and Development Center, Schenectady, 
New York. 

P. 65 (left, top to bottom) Magnion, Inc., 
Burlington, Mass.; Science Museum, London; 
General Electric Research & Development Center; 
(right) U.S. Steel Corp., Boston. 

P. 68 Dr. V. P. Hessler. 

P. 71 Radio Corporation of America. 

P. 73 Courtesy of B. Freudenberg, Inc., N.Y.C. 

P. 74 Freelance Photographs Guild, New York. 

P. 76 Deutsches Museum, Munich. 

P. 78 (portrait) The Royal Institution of Great 
Britain; (drawing) The Royal Institution of 
Great Britain. 

P. 85 Consolidated Edison Company of New 
York, Inc. 

P. 86 Tennessee VaUey Authority. 

P. 87 (top and bottom) Figuier, Louis, Les 
Nouvelles Conquetes de la Science, Paris, 1884. 

P. 88 (portraits) Thomas Alva Edison 
Foundation. 

P. 89 (patent) U.S. Patent Office Picture 
Collection. 

P. 94 (left) Tennessee Valley Authority; 
(right) Power Authority of the State of New York. 

P. 96 (left top) Westinghouse Electric Corp.; 
(left bottom) Edison Electric Institute, N.Y.C. 

P. 97 (power grid) Edison Electric Institute; 
(N.Y.C. at night) Con Edison of New York; 
(N.Y.C. blackout) Bob Gomel, LIFE MAGAZINE, 
© Time Inc. 

P. 99 Power Authority of the State of New York. 

P. 102Dr.V. P. Hessler. 

P. 1 12 American Institute of Physics. 

P. 117 Courtesy of Eastman Kodak Company. 

P. 118 (top left) McMath-Hulbert Observatory 
of University of Michigan; (top right) Harvard 
College Observatory; (bottom left) Sacramento 
Peak Observatory, Air Force Cambridge Research 
Laboratory. Photo courtesy of American Science 
and Engineering, Inc.; (bottom right) American 
Science and Engineering, Inc.; (center) Ball 
Brothers Research Corp., Boulder, Colorado. 

P. 119 (top left) U.S. Air Force Photo. Courtesy 
of News Photo Branch, Defense Information 
Service; (bottom left) American Science and 
Engineering, Inc.; (right, top to bottom) M.I.T. 
Lincoln Laboratory; ibid.; M.I.T. Lincoln Labora- 
tory by D. Downes, A. Maxwell and M. L. Meeks; 
from Science Year, The World Book Science 
Annual. © 1967 Field Enterprises Educational 
Corporation, Chicago. 

(continued on p. 130) 



Partial List of Staff and Consultants 

The individuals listed below (and on the following pages) have each contributed in some way to the 
development of the course materials. Their periods of participation ranged from brief consultations to 
full-time involvement in the team for several years. The affiliations indicated are those just prior to 
or during the period of participation. 



Advisory Committee 

E. G. Begle. Stanford University, Calif. 

Paul F. Brandwein. Harcourt. Brace & World. 

Inc.. San Francisco. Calif. 
Robert Brode. University of California. Berkeley 
Erwin Hiebert. University of Wisconsin, Madison 
Harr> Kelly. North Carolina State College, Raleigh 
William C. Kelly. National Research Council. 

Washington. DC. 
Philippe LeCorbeiller. New School for Social 

Research. New York. N.Y. 
Thomas Miner, Garden City High School. New 

York. 
Philip Morrison, Massachusetts Institute of 

Technology. Cambridge 
Ernest Nagel. Columbia University. New York, 

N.Y. 
Leonard K. Nash. Harvard University 
I. I. Rabi. Columbia Universitv. New York. N.Y. 



Staff and Consultants 

L. K. Akers. Oak Ridge Associated Universities, 

Tenn. 
Roger A. Albrecht, Osage Community Schools, 

Iowa 
David Anderson. Oberlin College. Ohio 
Gar\- Anderson. Harvard University 
Donald Armstrong, American Science Film 

Association. Washington. D.C. 
Arnold Arons. University of Washington 
Sam Ascher. Henry Ford High School, Detroit. 

Mich. 
Ralph Atherton. Talawanda High School, Oxford. 

Ohio 
Albert V. Baez. UNESCO, Paris 
William G. Banick. Fulton High School. Atlanta, 

Ga. 
Arthur Bardige. Nova High School. Fort 

Lauderdale. Fla. 
Rolland B. Bartholomew. Henr> M. Gunn High 

School. Palo Alto. Calif. 
O. Theodor Benfey. Earlham College, Richmond, 

Ind. 
Richard Berendzen. Harvard College Observatory 
Alfred M. Bork. Reed College, Portland, Ore. 
F. David Boulanger, Mercer Island High School, 

Washington 
Alfred Brenner. Harvard University 
Robert Bridgham. Harvard University 
Richard Brinckerhoff. Phillips Exeter Academy, 

Exeter, N.H. 



Donald Brittain. National Film Board of Canada, 

Montreal 
Joan Bromberg. Harvard University 
Vinson Bronson. Newton South High School. 

Newton Centre. Mass. 
Stephen G. Brush. Lawrence Radiation Laboratory, 

University of California, Livermore 
Michael Butler. CIASA Films Mundiales. S. A., 

Mexico 
Leon Callihan. St. Marks School of Texas, Dallas 
Douglas Campbell. Harvard University 
J. Arthur Campbell, Harvey Mudd College, 

Claremont, Calif. 
Dean R. Casperson, Harvard University 
Bobby Chambers, Oak Ridge Associated 

Universities, Tenn. 
Robert Chesley. Thacher School. Ojai. Calif. 
John Christensen. Oak Ridge Associated 

Universities, Tenn. 
Dora Clark. W. G. Enloe High School. Raleigh, 

N.C. 
David Clarke. Browne and Nichols School. 

Cambridge, Mass. 
Robert S. Cohen, Boston University, Mass. 
Brother Columban Francis, F.S.C., Mater Christi 

Diocesan High School. Long Island City. N.Y. 
Arthur Compton, Phillips Exeter Academy. 

Exeter. N.H. 
David L. Cone. Los Altos High School. Calif. 
William Cooley. University of Pittsburgh, Pa. 
Ann Couch. Harvard University 
Paul Cowan, Hardin-Simmons University, 

Abilene. Tex. 
Charles Davis, Fairfax County School Board. 

Fairfax, Va. 
Michael Dentamaro. Senn High School, Chicago. 

111. 
Raymond Dittman. Newton High School. Mass. 
Elsa Dorfman. Educational Services Inc.. 

Watertown. Mass. 
Vadim Drozin. Bucknell University, Lewisburg. 

Pa. 
Neil F. Dunn, Burlington High School. Mass. 
R. T. Ellickson. University of Oregon. Eugene 
Thomas Ernbn. Nova High School. Fort 

Lauderdale. Fla. 
Walter Eppenstein, Rensselaer Polytechnic 

Institute. Troy, N.Y. 
Herman Epstein. Brandeis University. Waltham, 

Mass. 
Thomas F. B. Ferguson. National Film Board of 

Canada. Montreal 
Thomas von Foerster, Harvard University 
Kenneth Ford, University of California, Irvine 

(continued on p. 132) 



Science is an adventure of the whole human race to learn to live in and 
perhaps to love the universe in which they are. To be a part of it is to 
understand, to understand oneself, to begin to feel that there is a capacity 
within man far beyond what he felt he had, of an infinite extension of 
human possibilities . . . 

I propose that science be taught at whatever level, from the lowest to the 
highest, in the humanistic way. It should be taught with a certain historical 
understanding , with a certain philosophical understanding , with a social 
understanding and a human understanding in the sense of the biography, the 
nature of the people who made this construction, the triumphs, the trials, the 
tribulations. 

I. I. RABI 

Nobel Laureate in Physics 



Preface 



Background The Project Physics Course is based on the ideas and 
research of a national curriculum development project that worked in 
three phases. First, the authors — a high school physics teacher, a 
university physicist, and a professor of science education — collaborated 
to lay out the main goals and topics of a new introductory physics 
course. They worked together from 1962 to 1964 with financial support 
from the Carnegie Corporation of New York, and the first version of 
the text was tried out in two schools with encouraging results. 

These preliminary results led to the second phase of the Project 
when a series of major grants were obtained from the U.S. Office of 
Education and the National Science Foundation, starting in 1964. 
Invaluable additional financial support was also provided by the 
Ford Foundation, the Alfred P. Sloan Foundation, the Carnegie 
Corporation, and Harvard University. A large number of collaborators 
were brought together from all parts of the nation, and the group 
worked together for over four years under the title Harvard Project 
Physics. At the Project's center, located at Harvard University, 
Cambridge, Massachusetts, the staff and consultants included college 
and high school physics teachers, astronomers, chemists, historians 
and philosophers of science, science educators, psychologists, 
evaluation specialists, engineers, film makers, artists and graphic 
designers. The teachers serving as field consultants and the students 
in the trial classes were also of vital importance to the success of 
Harvard Project Physics. As each successive experimental version of 
the course was developed, it was tried out in schools throughout the 
United States and Canada. The teachers and students in those schools 
reported their criticisms and suggestions to the staff in Cambridge, 
and these reports became the basis for the subsequent revisions of 
the course materials. In the Preface to Unit 1 Text you will find a list of the 
major aims of the course. 



We wish it were possible to list in detail the contributions of each 
person who participated in some part of Harvard Project Physics. 
Unhappily it is not feasible, since most staff members worked on a 
variety of materials and had multiple responsibilities. Furthermore, 
every text chapter, experiment, piece of apparatus, film or other item 
in the experimental program benefitted from the contributions of a 
great many people. On the preceding pages is a partial list of 
contributors to Harvard Project Physics. There were, in fact, many 
other contributors too numerous to mention. These include school 
administrators in participating schools, directors and staff members 
of training institutes for teachers, teachers who tried the course after 
the evaluation year, and most of all the thousands of students who 
not only agreed to take the experimental version of the course, but 
who were also willing to appraise it critically and contribute their 
opinions and suggestions. 

The Project Physics Course Today. Using the last of the experimental 
versions of the course developed by Harvard Project Physics in 
1964-68 as a starting point, and taking into account the evaluation 
results from the tryouts, the three original collaborators set out to 
develop the version suitable for large-scale publication. We take 
particular pleasure in acknowledging the assistance of Dr. Andrew 
Ahlgren of Harvard University. Dr. Ahlgren was invaluable because 
of his skill as a physics teacher, his editorial talent, his versatility 
and energy, and above all, his commitment to the goals of Harvard 
Project Physics. 

We would also especially like to thank Miss Joan Laws whose 
administrative skills, dependability, and thoughtfulness contributed so 
much to our work. The publisher, Holt, Rinehart and Winston, Inc. 
of New York, provided the coordination, editorial support, and general 
backing necessary to the large undertaking of preparing the final 
version of all components of the Project Physics Course, including 
texts, laboratory apparatus, films, etc. Damon, a company located in 
Needham, Massachusetts, worked closely with us to improve the 
engineering design of the laboratory apparatus and to see that it was 
properly integrated into the program. 

In the years ahead, the learning materials of the Project Physics 
Course will be revised as often as is necessary to remove remaining 
ambiguities, clarify instructions, and to continue to make the materials 
more interesting and relevant to students. We therefore urge all 
students and teachers who use this course to send to us (in care of 
Holt, Rinehart and Winston, Inc., 383 Madison Avenue, New York, 
New York 10017) any criticism or suggestions they may have. 



F. James Rutherford 
Gerald Holton 
Fletcher G. Watson 



Contents 



TEXT SECTION 



Prologue 



Chapter 13 Light 

Introduction 5 
Propagation of light 8 
Reflection and refraction 11 
Interference and diffraction 13 
Color 15 

Why is the sky blue? 20 
Polarization 21 
The ether 23 

Chapter 14 Electric and Magnetic Fields 

Introduction 31 

The curious properties of lodestone and amber: Gilbert's De Magnete 32 

Electric charges and electric forces 35 

Forces and fields 42 

The smallest charge 50 

Early research on electric charges 51 

Electric currents 53 

Electric potential difference 55 

Electric potential difference and current 58 

Electric potential difference and power 59 

Currents act on magnets 60 

Currents act on currents 62 

Magnetic fields and moving charges 66 

Chapter 15 Faraday and the Electrical Age 

The problem : getting energy from one place to another 75 

Faraday's early work on electricity and lines of force 76 

The discovery of electromagnetic induction 77 

Generating electricity by the use of magnetic fields : the dynamo 81 

The electric motor 84 

The electric hght bulb 86 

AC versus DC, and the Niagara Falls power plant 90 

Electricity and society 94 

Chapter 16 Electromagnetic Radiation 

Introduction 103 

Maxwell's formulation of the principles of electromagnetism 104 

The propagation of electromagnetic waves 107 

Hertz's experiments 111 

The electromagnetic spectrum 114 

What about the ether now? 121 

Epilogue 126 

Contents — Handbook Section 133 

Index/Text Section 180 

Index/Handbook Section 183 

Answers to End-of-Section Questions "l^e 

Brief Answers to Study Guide Questions 188 






*^- 



O;*^' 




■f 






ia^^vv 




\- 



:"♦ 



/ 



^, ^:x 







V. .-'• 



It was inconceivable to many sci- 
entists that one body could directly 
affect another across empty space. 
They devised a variety of schemes to 
fill the space in betvi^een wWh some- 
thing that would transmit the effect 
first with material "ether." — later with 
mathematical "fields." Some of these 
schemes are illustrated on this 
page. Descartes, 17th century (bottom 
left); Euler, 18th century (top left); 
Maxwell, 19th century (top right). 
Above is a drawing copied from The 
New York Times (1967) representing 
the magnetic field around the earth. 
It is not the more symmetrical field the 
earth would have on its own, but as 
disturbed by the field due to streams 
of charged particles from the sun. 



UNIT 



4 



Light and 
Electromagnet ism 



CHAPTERS 

13 Light 

14 Electric and Magnetic Fields 

15 Faraday and the Electric Age 

16 Electromagnetic Radiation 



PROLOGUE The conviction that the world, and all that is in it. 
consist of matter in motion drove scientists to search for mechanical 
models that could account for light and electromagnetism. That is, they 
tried to imagine how the effects of light, electricity, and magnetism 
could be explained in detail as the action of some material objects. 
(For example, the way light bounces off a mirror might be understood 
if one imagines light to consist of particles that have some properties 
similar to those of little balls.) Such mechanical models were useful for 
a while, but in the long run had to be given up as far too limited. This 
search, what was discovered, and the changes these discoveries 
initiated in science-in technology and in society-form the subject 
of this unit. In this Prologue we sketch the development of some of 
these models and briefly indicate the effect of these developments on 
our present ideas of the physical world. 

From the seventeenth century on there were two competing models 
for light, one depicting light as particles, the other depicting light as 
waves. In the first half of the nineteenth century the wave model won 
general acceptance, because if was better able to account for newly 
discovered optical effects. Chapter 13 tells the story of the triumph of 
the wave theory of light. The wave theory maintained its supremacy 
until the early part of the twentieth century, when it was found (as we 
shall see in Unit 5) that neither waves nor particles alone were sufficient 
to account for all the behavior of light. 

As experiments established that electric and magnetic forces have 
some characteristics in common with gravitational forces, theories of 
electricity and magnetism were developed which were modeled on 
Newton's treatment of gravitation. The assumption that there are forces 
between electrified and magnetized bodies which vary inversely with 

1 



Light and Electromagnetism 



This letter is reproduced exactly 
as Newton wrote it. 



the square of the distance was found to account for many observations. 
The drafters of these theories assumed that bodies can exert forces 
over a distance without the necessity for one body to touch another. 

Although action at-a-distance theories were remarkably successful 
in providing a quantitative explanation for some aspects of electro- 
magnetism, these theories did not at the time provide a comprehensive 
explanation. Instead, the means of description that became widely 
accepted by the end of the nineteenth century, and that is now generally 
believed to be the best way to discuss all physical forces, is based on 
the idea of fields, an idea that we introduce in Chapter 14 and develop 
further in the last chapter of the unit. 

Many scientists felt that action-at-a-distance theories, however 
accurate in prediction, failed to give a satisfactory physical explanation 
for how one body exerts a force on another. Newton himself was re- 
luctant to assume that one body can act on another through empty 
space. In a letter to Richard Bentley he wrote: 

Tis unconceivable to me that inanimate brute matter 
should (without the meditation of something else wch is not 
material) operate upon & affect other matter without mutual 
contact: . . . And this is one reason why I desire you would 
not ascribe innate gravity to me. That gravity should be 
innate inherent & essential to matter so yt one body may act 
upon another at a distance through a vacuum wthout the 
mediation of any thing else by & through wch their action or 
force may be conveyed from one point to another is to me so 
great an absurdity that I believe no man who has in philo- 
sophical matters any competent faculty of thinking can ever 
fall into it. 



William Thomson (Lord Kelvin) was 
a Scottish mathematical physicist 
who contributed to the fields of 
electricity, mechanics, and thermo- 
dynamics and to such practical 
developments as an improved 
ship's compass and the first Atlantic 
cable. The Kelvin scale of absolute 
temperature is named for him. 



Some seventeenth-century scientists, less cautious in their 
published speculations than Newton was, proposed that objects are 
surrounded by atmospheres that extend to the most distant regions and 
serve to transmit gravitational, electric and magnetic forces from one 
body to another. The atmospheres proposed at this time were not made 
a part of a quantitative theory. In the nineteenth century, when the 
idea of an all-pervading atmosphere was revived, numerous attempts 
were made to develop mathematically the properties of a medium that 
would transmit the waves of light. The name "luminiferous ether" was 
given to this hypothetical "light-bearing" substance. 

The rapid discovery of new electrical and magnetic effects in the 
first half of the nineteenth century acted as a strong stimulus to 
scientific imagination. Michael Faraday (1791-1867). who made many 
of the important discoveries, developed a model with assigned lines of 
force to the space surrounding electrified and magnetized bodies. 
Faraday showed how these lines of force could be used to account for 
many electromagnetic effects. 

In a paper he wrote at age 17, William Thomson (1824-1907) showed 
how the equations used to formulate and solve a problem in electro- 
statics, could also be used to solve a problem in the flow of heat. At 
that time electrostatics was most simply and effectively treated by 



Prologue 



considering that electrical forces can act at a distance, while the flow 
of heat was generally held to result from the action of parts that touch. 
With this paper Thomson showed that the same mathematical formula- 
tion could be used for theories based on completely different physical 
assumptions. Perhaps, then, it was more important to find correct 
mathematical tools than it was to choose a particular mechanical model. 

James Clerk Maxwell (1831-1879), inspired by Faraday's physical 
models and by Thomson's mathematical demonstrations, undertook the 
task of developing a mathematical theory of electromagnetism. From 
the assumption of an imaginary ether filled with gears and idler wheels. 
Maxwell gradually worked his way to a set of equations that described 
the properties of electric and magnetic fields. These equations were 
later found to be remarkably successful. Not only did the equations 
describe accurately the electric and magnetic effects already known to 
occur, but they led Maxwell to predict new effects based on the idea 
of a propagating wave disturbance in electric and magnetic fields. 
The speed he predicted from such electromagnetic waves was nearly 
the same as the measured speed of light, which suggested to him that 
light might be an electromagnetic wave. 

The field concept, in conjunction with the concept of energy, 
provides a way of treating the action of one body on another without 
speaking of action at a distance or of a material medium that transmits 
the action from one body to another. The concept of a field has proved 
its utility over and over again during the twentieth century. 



See Maxwell's article "Action at a 
Distance" in Reader 4. 




Radio telescope at the National Radio 
Astronomy Observatory, Greenbank, 
West Virginia. 



13.1 


Introduction 


5 


13.2 


Propagation of light 


8 


13.3 


Reflection and refraction 


11 


13.4 


Interference and diffraction 


13 


13.5 


Color 


15 


13.6 


Why is the sky blue? 


20 


13.7 


Polarization 


21 


13.8 


The ether 


23 



CHAPTER THIRTEEN 



Light 



13.1 Introduction 



What is light? At first glance, this may seem to be a rather 
trivial question. After all, there is hardly anything that is more 
familiar to us. We see by means of light. We also live by light, for 
without it there would be no photosynthesis, and photosynthesis is 
the basic source of energy for most forms of life on earth. Light is 
the messenger which brings us most of our information about the 
world around us, both on the earth and out to the most distant 
reaches of space. Because our world is largely defined by light, we 
have always been fascinated by its behavior. How fast does it 
travel? How does it travel across empty space? What is color? 

To the physicist, light is a form of energy. He can describe light 
by measurable values of speed, wavelengths or frequencies, and 
intensity of the beam. To him, as to all people, light also means 
brightness and shade, the beauty of summer flowers and fall 
foliage, of red sunsets and of the canvases painted by masters. 
These are different ways of appreciating light: one way is to regard 
its measurable aspects — which has been enormously fruitful in 
physics and in technology. The other is to ask about the aesthetic 
responses in us when we view the production of light in nature or 
art. Still another way of considering light is in terms of the bio- 
physical process of vision. 

Because these aspects of light are not easily separated, problems 
raised about light in the early history of science were more subtle 
and more elusive than those associated with most other aspects of 
our physical experience. Early ideas on its nature were confused by 
a failure to distinguish between light and vision. This confusion is 
still evident in young children. When playing hide-and-go-seek, 
some of them "hide" by covering their eyes with their hands; 
apparently they think that they cannot be seen when they cannot 
see. The association of vision with light persists into the language 
of the adult world. We talk about the sun "peeping out of the clouds" 
or the stars "looking down." 




Behold the Light emitted from 
the Sun, 

What more familiar, and what 
more unknown; 

Whlle by its spreading Radiance 
it reveals 

All Nature's Face, it still itself 
conceals . . . 

[Richard Blackmore. Creation II, 1715.] 



SG 13.1 



Light 



There is no sharp general distinction 
among model, hypothesis, and 
theory. Roughly we can say that a 
model (whether mechanical or 
mathematical) is a rather limited 
conception to explain a particular 
observed phenomenon; a hypoth- 
esis is a statement that usually 
may be directly or indirectly tested; 
a theory is a more general construe 
tion, putting together one or more 
models and several hypotheses to 
explain many previously apparently 
unrelated effects or phenomena. 



Some of the Greek philosophers beheved that hght travels in 
straight lines at high speed, and that it contains particles which 
stimulate the sense of vision when they enter the eye. For centuries 
after the Greek era, during which limited attention was paid to the 
nature of light, the particle model persisted. However, around 1500 
Leonardo da Vinci, noting a similarity between sound echoes and 
the reflection of light, speculated that light might have a wave 
character. 

A decided difference of opinion emerged among scientists of the 
seventeenth century about the nature of light. Some, including 
Newton, favored a model largely based on the idea of light as a 
stream of particles. Others, including Huygens, supported a wave 
model. By the late nineteenth century, however, there appeared to 
be overwhelming evidence that the observed characteristics of 
light could be explained by assuming that it had the nature of a 
wave motion; that is, by assuming a wave model. In this chapter 
we shall look at the question How appropriate is a wave model in 
explaining the observed behavior of light? That is, we shall take 
the wave model as a hypothesis, and examine the evidence that 
supports it. We must bear in mind that any scientific model, 
hypothesis or theory has two chief functions — to explain what is 
known, and to make predictions that can be subjected to experi- 
mental test. We shall look at both of these aspects of the wave 
model. The result will be very curious. The wave model turns out 
to work splendidly for all the properties of light known before the 
twentieth century. But in Chapter 18 we will find that for some 
purposes we must adopt a particle model. Then in Chapter 20 we 
will combine both models, joining together two apparently opposite 
theories. 

We have already mentioned the ancient opinion — later proved 
by experiment -that light travels in straight lines and at high 
speed. Our daily use of mirrors convinced us that light can also be 
reflected. There are other characteristics of light — for example, it 
can be refracted, and it shows the phenomena of interference and 
diffraction. All of these properties you have studied earlier, when 
looking at the behavior of waves in Chapter 12. If necessary, it 
would therefore be well to refresh your memory about the basic 
ideas of that chapter before going on to the study of light. We shall, 
however, look also at some other phenomena — dispersion, polariza- 
tion and scattering -which so far we have given little or no 
consideration. As we shall see, these also will fit into our wave 
model, and in fact will constitute strong experimental support 
for it. 

Before going on to a discussion of these various characteristics 
of light's behavior and how they provide evidence in support of 
our hypothesis of a wave model for light, we shall first consider 
the propagation of light and two characteristics — reflection and 
refraction -which can be explained by both a corpuscular (particle) 
model and a wave model. The discussion in this text must, of 
course, be supplemented by experiments in your laboratory session 



Light beams travel in straight lines 




8 



Light 



and wherever possible also by activities, selections from the 
readers, films and loops, transparencies, etc. 

Indeed, this is a good moment to remind you of an important 
point: this course stresses the use of many media to learn physics. 
It therefore differs from many other courses with which you may 
be familiar, and which rely most heavily on a text only. In this 
course, on the contrary, the text will sometimes only motivate or 
put into context a part of the course that is much better learned by 
doing experiments, by class discussion etc., than by reading about 
them. This is particularly the case with optics, the science of light, 
and with electricity and magnetism — the subjects of Unit 4. This 
text will merely give a general map which you will fill out in a way 
that makes the study of physics more valid and exciting than 
reading alone. 



SG 13.2 



Camera obscura is a Latin phrase 
meaning "dark chamber." 



First published illustration of a camera 
obscura. observing a solar eclipse in 
January 1544, from a book by the 
Dutch physician and mathematician 
Gemma Frisius. 



13.2 Propagation of light 

There is ample evidence that light travels in straight lines. The 
fact that one cannot see "around the corner" of an obstacle is one 
obvious example. The outline of a shadow cast by the sun is but one 
example of the sharply defined shadows cast by a large but very 
distant source. Similarly, sharp shadows are cast by a closer source 
of small dimensions. The distant sun or the nearby small source are 
approximate point sources of light; it is from such point sources 
that we get sharp shadows. 

Images as well as shadows can demonstrate that light travels 
in straight lines. Before the invention of the modern camera with 
its lens system, a light-tight box with a pinhole in the center of one 
face was widely used. As the camera obscura, the device was highly 
popular in the Middle Ages. Leonardo da Vinci probably used it as 
an aid in his sketching. In one of his manuscripts he says that "a 
small aperture in a window shutter projects on the inner wall of the 
room an image of the bodies which are beyond the aperture," and 
he includes a sketch to show how the straight-line propagation of 
light explains the formation of an image. 




It is often convenient to use a straight line to represent the 
direction in which light travels. The convenient pictorial device of 
an infinitely thin ray of light is useful for thinking about light, but 
it does not correspond directly to anything that actually exists. A 



Section 13.2 



light beam emerging from a good-sized hole in a screen is as wide 
as the hole. You might expect that if we made the hole extremely 
small we would get a very narrow beam of light — ultimately, just 
a single ray. But we don't! Diffraction effects (such as you have 
already observed for water and sound waves) appear when the 
beam of light passes through a small hole (see below). So an 
infinitely thin ray of light, although it is pictorially useful, cannot 
be produced in practice. But we can still use the idea to represent 
the direction in which a train of parallel waves is traveling. 




Given that light seems to travel in straight lines, can we tell 
how fast it goes? Galileo discussed this problem in his Two New 
Sciences book (published 1638). He pointed out that everyday 
experiences might lead us to conclude that the propagation of light 
is instantaneous. But these experiences, when analyzed more 
closely, really show only that light travels much faster than sound. 
For example, "when we see a piece of artillery fired, at a great 
distance, the flash reaches our eyes without lapse of time; but the 
sound reaches the ear only after a noticeable interval." But how do 
we really know whether the light moved "without lapse of time" 
unless we have some accurate way of measuring the lapse of time? 

Galileo then described an experiment by which the speed of 
light might be measured by two persons on distant hills flashing 
lanterns. (This experiment is to be analyzed in SG 13.4.) He 
concluded that the speed of light is probably finite, not infinite, but 
he was not able to estimate a definite value for it. 

Experimental evidence was first successfully related to a finite 
speed for light by a Danish astronomer, Ole Homer. Detailed 
observations of Jupiter's satellites had shown an unexplained 
irregularity in the times between eclipse of the satellite by Jupiter's 
disk. In September of 1676, Romer announced to the Academy of 
Sciences in Paris that the eclipse of a satellite of Jupiter, which was 
expected to occur at 45 seconds after 5:25 a.m. on the ninth of 
November, would be ten minutes late. On November 9, 1676. 
astronomers at the Royal Observatory in Paris, though skeptical of 
Romer's mysterious prediction, made careful observations of the 
eclipse and reported that it did occur late, just as Romer had 
predicted. 



An attempt to produce a ray" of 
light. To make the pictures at the left, 
a parallel beam of red light was di- 
rected through increasingly narrow 
slits to a photographic plate. (Of 
course, the narrower the slit, the less 
the light that gets through. This was 
compensated for by longer exposures 
in these photographic exposures.) 
The slit widths, from left to right, were 
15 mm, 0.7 mm, 0.4 mm, 0.2 mm. and 
0,1 mm. 



SG 13.3 



SG 13.4 



10 



Light 



As often happens, modern historian 
of science have cast some doubt o 
the exactness of Rbmer's calcula- 
tion of the time interval and on the 
observation of the time of the 
eclipse. Nevertheless, the impor- 
tance of Rbmer's work was not so 
much that it led to a particular value 
of the speed of light, but rather tha; 
it established that the propagation 
of light is not instantaneous but 
takes a finite time. 



SG 13.5 



SG 13.6 



Later, Romer revealed the theoretical basis of his prediction to 
the baffled astronomers at the Academy of Sciences. He explained 
that the originally expected time of the eclipse had been calculated 
on the basis of observations made when Jupiter was near the earth. 
But now Jupiter had moved to a distant position. The delay in the 
eclipse was simply due to the fact that light from Jupiter takes time 
to reach the earth, the time interval depending on the relative 
positions of Jupiter and the earth in their orbits. In fact, he 
estimated that it takes about 22 minutes for light to cross the 
earth's own orbit around the sun. 

Shortly thereafter, the Dutch physicist Christiaan Huygens used 
Romer"s data to make the first calculation of the speed of light. He 
combined Homers value of 22 minutes for light to cross the earth's 
orbit with his own estimate of the diameter of the earth's orbit. 
(This distance could be estimated for the first time in the seven- 
teenth century, as a result of the advances in astronomy described 
in Unit 2.) Huygens obtained a value which, in modem units, is 
about 2 X 10* meters per second. This is about two-thirds of the 
presently accepted value (see below). The error in Huygen's value 
was due mainly to Romer's overestimate of the time interval — we 
now know that it takes light only about 16 minutes to cross the 
earth's orbit. 

The speed of light has been measured in many different ways 
since the seventeenth century. (See the article "Velocity of Light" 
in Reader 4.). Since the speed is ver\' great, it is necessary to use 
either a very long distance or a very short time interval or both. 
The earlier methods were based on measurements of astronomical 
distances. In the nineteenth century, rotating slotted wheels and 
mirrors made it possible to measure very short time intervals so 
that distances of a few miles could be used. The development of 
electronic devices in the twentieth century allows measurement of 
even shorter time intervals. Consequently the speed of light is one 
of the most accurately known physical constants; but because of 
the importance of the value of the speed of light in modem physical 
theories, physicists are continuing to improve their methods of 
measurements. 

As of 1970, the most accurate measurements indicate that the 
speed of light in vacuum is 299,792,500 meters per second. The 
uncertainty of this value is thought to be less than 300 meters per 
second, or 0.0001%. The speed of light is usually represented by the 
symbol c. and for most purposes it is sufficient to use the 
approximate value c = 3 x 10* meters per second. 



Q1 Can a beam of light be made increasingly narrow by 
passing it through narrower and narrower slits? 

Q2 What reason did Romer have for thinking that the eclipse 
of a particular satellite of Jupiter would be observed later than 
expected? 

Q3 What was the most important outcome of Romer's work? 



Section 13.3 



11 



13.3 Reflection and refraction 

What happens when a ray of hght traveling in one medium (say 
air) hits the boundary of another medium (say glass)? The answers 
to this question depend on whether we adopt a particle or a wave 
theory of light and, therefore, give us a chance to test which theon,' 
is better. 

We have already discussed reflection and refraction from the 
wave viewpoint in Chapter 12, so we need only recall the results 
obtained there. 

1. A ray may be taken as the line drawn perpendicular to a 
wave's crest lines; a ray represents the direction in which a train 
of parallel waves is traveling. 

2. In reflection, the angle of incidence (6,) is equal to the 
angle of reflection (^r)- 

3. Refraction involves a change of wavelength and speed of 
the wave as it goes into another medium. In particular, when the 
speed decreases the wavelength decreases, and the ray is bent in a 
direction toward a line perpendicular to the boundary'. This bending 
toward the peipendicular is observed when a ray of light goes from 
air to glass. 




What about the particle model? To test this model, we must 
first consider the nature of the surface of glass. Though apparently 
smooth, it is actually a wrinkled surface. By means of a powerful 
microscope, it can be seen to have endless hills and valleys. If 
particles of light hit such a wrinkled surface, they would be 
scattered in all directions, not reflected and refracted as shown in 
the above figures. Therefore, Newton argued, there must actually 
be "some feature of the body which is evenly diffused over its 
surface and by which it acts upon the ray without immediate 
contact." Obviously this force was one which repelled the particles 
of light. A similar force, which attracted light particles instead of 
repelling them, could be used to explain refraction. As a particle of 
light approached a boundary of another medium, it would first have 
to overcome the repulsive force; if it did that, it would then meet 
an attractive force in the medium which would pull it into the 
medium. Since the attractive force would be a vector with a 




Two narrow beams of light, coming 

from the upper left, strike a block of 

glass. Can you account for the other 

effects? 

SG 13.7-13.12 

The incident, reflected, and refracted 
rays are all in the same plane, a 
;!ane perpendicular to the surface. 




12 



Light 



The surface of a mirror as shown by 
an electron microscope. The surface 
is a three-micron thick aluminum film. 
The magnification here is nearly 
26,000. (m stands for micron; where 
1/x= 10'' meter.) 




SG 13.13 




component in the direction of the original motion of the ray, the 
hght particle's speed would increase. So if the ray were moving at 
an oblique angle to the boundary, its direction would change as it 
entered the medium, toward the line perpendicular to the boundary. 

According to the particle model, therefore, we can make the 
following statements about reflection and refraction. 

1. A ray represents the direction in which the particles are 
moving. 

2. In reflection, the angles of incidence and reflection are 
equal. This prediction can be derived from the Law of Conservation 
of Momentum (Chapter 9) applied to the interaction of the particles 
with the repulsive power of the medium. 

3. Refraction involves a change of speed of the particles as 
they go into another medium. In particular, when an attractive 
power acts, the speed increases and the ray is bent into the 
medium. 

Comparing these features of the particle model with the 
corresponding features of the wave model (above), we find that the 
only difference is in the predicted speed for a refracted ray. When 
we observe that a ray is bent toward the perpendicular line on 
going into another medium — as is the case for light going from air 
into water — then the particle theory predicts that light has a greater 
speed in the second medium, whereas the wave theory predicts that 
light has a lower speed. 

You might think that it would be fairly easy to devise an 
experiment to determine which prediction is correct. All one has to 
do is measure the speed of light in water to compare it with the 
speed of light in air. However, in the late seventeenth and early 
eighteenth centuries, when the wave model was supported by 
Huygens and the particle model by Newton, no such experiment 



Section 13.4 



13 



was possible. Remember that at that time the only available way 
of measuring the speed of light was an astronomical one. Not 
until the middle of the nineteenth century did Fizeau and Foucault 
measure the speed of light in water. The results agreed with the 
predictions of the wave model: the speed of light is less in water 
than in air. 

Ironically, by the time these experiments were done, most 
physicists had already accepted the wave model for other reasons 
(see below). The Foucault-Fizeau experiments of 1850 were widely 
regarded as driving the last nail in the coffin of the Newtonian 
particle theory. 

Q4 What evidence showed conclusively that Newton's particle 
model for light could not explain all aspects of refraction? 

Q5 If light has a wave nature, what changes take place in the 
speed, wavelength, and frequency of light on passing from air 
into water? 



13.4 Interference and diffraction 

From the time of Newton until the early years of the nineteenth 
century, the particle theory of light was favored by most physicists, 
largely because of the prestige of Newton. Early in the nineteenth 
century, however, the wave theory was revived by Thomas Young. 
He found, in experiments made between 1802 and 1804, that light 
shows the phenomenon of interference. Interference patterns have 
been discussed in Sec. 12.6 in connection with water waves. Such 
patterns could not easily be explained by the particle theory of 
light. Young's famous "double-slit experiment" must be done in the 
lab rather than talked about; it provides convincing evidence that 
light has properties that can be explained only in terms of waves. 

When a beam of light is split into two beams, and the split 
beams are then allowed to overlap, we find that the two wave trains 
interfere constructively in some places and destructively in others. 
To simplify the interpretation of the experiment, we will assume 




Thomas Young (1773-1829) was an 
English linguist, physician, and expert 
in many fields of science. At the age of 
fourteen he was familiar with Latin, 
Greek, Hebrew, Arabic, Persian, 
French, and Italian, and later was one 
of the first scholars successful at de- 
coding Egyptian hieroglyphic inscrip- 
tions. He studied medicine in England, 
Scotland, and Germany. While still in 
medical school he made original 
studies of the eye. and later developed 
the first version of what is now known 
as the three-color theory of vision. He 
also did research in physiology on the 
functions of the heart and arteries, 
and studied the human voice mecha- 
nism, through which he became in- 
terested in the physics of sound and 
sound waves. 




Young then turned to optics, and 
showed that many of Newton's experi- 
ments with light could be explained in 
terms of a simple wave theory of light. 
This conclusion was strongly attacked 
by some scientists in England who 
were upset by the implication that 
Newton might be wrong. 



Thomas Youngs original drawing 
showing interference effects in over- 
lapping waves. The alternate regions 
of reinforcement and cancellation in 
the drawing can be seen best by plac- 
ing your eye near the right edge and 
sighting at a grazing angle along the 
diagram. 



14 



Light 



A Polaroid photograph taken through 
a Project Physics magnifier placed 
about 30 cm behind a pair of closely 
spaced slits. The slits were illuminated 
with a narrow but bright light source. 




SG 13.14 




Augustin Jean Fresnel (1788-1827) 
was an engineer of bridges and roads 
for the French government. In his 
spare time he carried out extensive 
experimental and theoretical work in 
optics. Fresnel developed a compre- 
hensive wave model of light that suc- 
cessfully accounted for reflection, 
refraction, interference, and polariza- 
tion. He also designed a lens system 
for lighthouses that is still used today. 



that the experiment is done with hght that has a single definite 
wavelength X. 

Young used a black screen with a small hole punched in it to 
produce a narrow beam of sunlight in a dark room. In the beam 
he placed a second black screen with two narrow slits cut in it, 
close together. Beyond this screen he placed a white screen. The 
light coming through each slit was diffracted and spread out into 
the space beyond the screen. The light from each slit interfered 
with the light from the other, and the interference pattern could be 
seen where the light fell on the white screen. Where interference 
was constructive, there was a bright band on the screen. Where 
interference was destructive, the screen remained dark. 

The fact that Young could actually find, by experiment, 
numerical values for the exceedingly short wavelength of light was 
quite astonishing. Here is his result: 

From a comparison of various experiments, it appears 
that the breadth of the undulations constituting the 
extreme red light must be supposed to be, in air, about 
one 36 thousandth of an inch, and those of the extreme 
violet about one 60 thousandth. 

When Young announced his results that were based on the 
wave theory of light, he took special pains to show that Newton 
himself had made several statements favoring a theory of light 
that had some aspects of a wave theory even though Newton was 
generally considered a supporter of the particle theory. Neverthe- 
less, Young was not taken seriously. It was not until 1818, when the 
French physicist Augustin Fresnel proposed a mathematical wave 
theory of his own, that Young's research began to get the credit it 
deserved. Fresnel also had to submit his work for approval to a 
group of physicists who were committed to the particle theory of 
light. One of them, the mathematician Simon Poisson, took Fresnel's 
wave equations and showed that if these equations really did 
describe the behavior of light, a very peculiar thing ought to happen 
when a small solid disk is placed in a beam of light. A white screen 
placed at certain distances behind the disk should have a bright 
spot in the center of the shadow, because diffraction of the light 
waves all around the edge of the round disk should lead to construc- 
tive interference at the center. In the particle theory of light, there 
was no room for ideas such as diffraction and constructive inter- 
ference, and there could be no such bright spot. Since such a bright 
spot had never been reported, and furthermore since the idea of a 
bright spot in the center of a shadow sounded absurd on the face 
of it, Poisson announced gleefully to Fresnel that he had refuted 
the wave theory. 

Fresnel accepted the challenge, however, and immediately 
arranged for this prediction to be tested by experiment. The result 
was that he could demonstrate that there was a bright spot in the 
center of the shadow, as predicted by Poisson on the basis of 
f resnel's wave theory. 

When the significance of the Young double-slit experiment and 



Section 13.5 



15 




the Poisson bright spot was reahzed, support for the particle theory 
of hght began to crumble away. By 1850 the validity of the wave 
model of light was generally accepted, and physicists had begun to 
concentrate on working out the mathematical consequences of this 
model and its application to all the different properties of light. 



Diffraction pattern due to an opaque 
circular disk, showing the Poisson 
bright spot in the center of the shad- 
ow. Note also the bright and dark 
fringes of constructive and destructive 
interference. (You can make similar 
photographs yourself — see the activ- 
ity "Poisson's Spot" in the Handbook.) 



SG 13.15 



How did Young's experiments support the wave model of 



Q6 
light? 

Q7 In what way is diffraction involved in Young's experiments? 

Q8 What phenomenon was predicted by Poisson on the basis 
of Fresnel's wave theory? 



13.5 Color 

Man's early appreciation of color survives for our contemplation 
in the coloring agents found in prehistoric painting and pottery. But 
no scientific theory of color was developed before the time of 
Newton. Until then, most of the commonly accepted ideas about 
color had been advanced by artist-scientists, like da Vinci, who 
based their ideas on experiences with mixing pigments. 

Unfortunately, the lessons learned in mixing pigment can 
rarely be applied to the mixing of colors of light. In early times, it 
was thought that light from the sun was "pure light," and that -as 
by refraction in glass -color came from adding impurity to this 
pure light. 

Newton became interested in colors while he was still a student 
at Cambridge University, when he set out to construct an astro- 





Diffraction and Detail 

The photograph on the left shows the dif- 
fraction image of a point source of light. 
Diffraction by the camera lens opening 
has spread the light energy into a bright 
central disk surrounded by alternate dark 
and bright rings. The photographs below 
show an array of point sources, recorded 
through a progressively smaller and 
smaller hole. The array could represent 
a star cluster, surface detail on Mars, 
granules in living cells or simply specific 
points on some object. 
The diffraction of the waves from the 
edges of the hole limits the detail of in- 
formation that it is possible to receive. As 
the hole through which we observe the 
array below becomes smaller, the dif- 
fraction image of each point spreads out 
and begins overlapping the diffraction 
images of other points. When the diffrac- 
tion patterns for the points overlap suffi- 
ciently, it is impossible to distinguish 
between them. 

This problem of diffraction has many 
practical consequences. We obtain most 
of the information about our environment 
by means of waves (light, sound, radio, 
etc.) which we receive through some sort 
of hole: the pupil of the eye. the entrance 
to the ear or a microphone, the aperture 
of an optical telescope or radio telescope, 
etc. In all these cases, then, diffraction 
places a limit on the detail with which the 
sources of waves can be discriminated. 




Section 13.5 



17 



nomical telescope. One of the troublesome defects of the telescope 
was a fuzzy colored edge that always surrounded the Image 
formed by the telescope lens. It was perhaps in an attempt to 
understand this particular defect that he began his extensive study 
of color. 

In 1672, at the age of 29, Newton published a theory of the 
nature of color in the Philosophical Transactions of The Royal 
Society of London. This was his first published scientific paper. 
He wrote: 



... in the beginning of the Year 1666 (at which time I 
applyed myself to the grinding of Optick glasses of other 
figures than Spherical,) I procured me a Triangular 
glass-Prisme, to try therewith the celebrated Phaenom- 
ena of Colours. And in order thereto haveing darkened 
my chamber, and made a small hole in my window-shuts, 
to let in a convenient quantity of the Suns hght, I placed 
my Prisme at his entrance, that it might be thereby 
refracted to the opposite wall. It was at first a very pleas- 
ing divertisement, to view the vivid and intense colours 
produced thereby .... 




The cylindrical beam of "white" sunlight from the circular 
opening passed through the prism and produced on the opposite 
wall an elongated patch of colored light, violet at one end, red at 
the other and showing a continuous gradation of colors in between. 
For such a pattern of colors, Newton invented the name spectrum. 

But, Newton asked himself, from where do the colors come, 
and why is the image spread out in an elongated patch rather than 
circular? Seeking an explanation, Newton passed the hght through 
different thicknesses of the glass, changed the size of the hole in 
the window shutter, and even placed the prism outside the window. 
But he found that none of these changes in conditions had any 
effect on the spectrum. To test whether some unevenness or 
irregularity in the glass produced the specti-um, he passed the 
colored rays from one prism through a similar second prism turned 
upside down. If some irregularity in the glass was responsible for 
spreading out the beam of hght, then passing this beam through 
the second prism should spread it out even more. Instead, the 
second prism, when properly placed, served to bring the colors back 
together fairly well to form a spot of white light, as if the hght 
had not passed through either prism. 

By such a process of elimination, Newton convinced himself of 



The drawing at the left is based on 
Newton's diagram of the refraction of 
sunlight by a prism. 



As is suggested in the diagram below, 
the recombination of colors by a sec- 
ond prism is not complete. Newton 
himself noted: "The prisms also must 
be placed very near to one another; 
for if their distance be so great, the 
colours begin to appear in the light, 
before its incidence on the second 
prism, these colours will not be de- 
stroyed by the contrary refractions of 
that prism." 







18 Light 

a belief that he probably had held from the beginning: white light 
is composed of colors. It is not the prism that manufactures or adds 
the colors: they were there all the time, but mixed up so that they 
could not be distinguished. When white light passes through a 
prism, each of the component colors is refracted at a different 
angle, so that the beam is spread into a spectrum. 

As a further test of this hypothesis. Newton cut a small hole 
in a screen on which a spectrum was projected, so that light of a 
single color could be separated out and passed through a second 
prism. He found that the second prism had no further effect on 
this single-color beam, aside from refracting it more. Once the first 
prism had done its job of separating the colored components of 
white light, the second prism could not change the color of the 
components. 

Summarizing his conclusions. Newton wrote: 

Colors are not Qualifications of Light derived from 
Refraction or Reflection of natural Bodies (as 'tis gen- 
erally believed) but Original and Connate Properties, 
which in divers Rays are divers. Some Rays are disposed 
to exhibit a Red Colour and no other: some a Yellow and 
no other, some a Green and no other, and so of the rest. 
Nor are there only Rays proper and particular to the more 
Eminent Colours, but even to all their inteiTnediate 
gradations. 

Apparent colors of objects. So far Newton had discussed only 
the colors of rays of light, but in a later section of his paper he 
raised the important question: why do objects appear to have 
different colors? Why is the sky blue, the grass green, a paint- 
pigment yellow or red? Newton proposed a very- simple answer: 

That the Colours of all Natural Bodies have no other 
Origin than this, that they . . . Reflect one sort of Light 
in greater plenty than another. 

In other words, a red pigment looks red to us because when white 
sunlight falls on it. the pigment absorbs most of the rays of other 
colors of the spectioim and reflects mainly the red to our eyes. 
According to Newtons theory-, color is not a property of an 
object by itself, but depends on how the object reflects and absorbs 
the various colored rays that strike it. Newton justified this 
hypothesis by pointing out that an object may appear to have a 
different color when a different kind of light shines on it. For 
example, consider a pigment that reflects much more red light than 
green or blue light. When illuminated by white light, it will reflect 
mostly the red component of the white light, so it will appear red. 
But if it is illuminated with blue light, there is no red for it to 
reflect: it will reflect only very little of the blue light, so it will 
appear to be dark and slightly blue. Newton wrote: 

I have experimented in a dark Room, by illuminating 
those Bodies with uncompounded (pure) light of divers 
Colours. For bv that means anv Bodv mav be made to 



Section 13.5 



19 



appear of any Colour. They have there no appropriate 
Colour, but ever appear of the Colour of the Light cast 
upon them, but yet with this difference, that they are 
most brisk and vivid in the Light of their own Day-light 
Colour. 

Reactions to Newton's theory. Newton's theory of color met with 
violent opposition at first. Other British scientists, especially Robert 
Hooke, objected that postulating a different kind of light for each 
color was unnecessary. It would be simpler to assume that the 
different colors were produced from pure white hght by some kind 
of modification. Hooke, for example, proposed a color theory based 
on the wave model of light: ordinarily, in white light, the wave 
front is perpendicular to the direction of motion. (See Sec. 12.5 for 
a definition of wave front.) Colors are produced, according to Hooke, 
when refraction by another medium twists the wave front so that it 
is no longer perpendicular to the direction of motion. 

Newton was aware of the fallacies in Hooke's theory, but he 
disliked public controversy. In fact, he waited until after Hooke's 
death in 1703 to publish his own book, Opticks (1704), in which he 
reviewed the properties of light. 

While Newton's Principia was a much more important work 
from a purely scientific viewpoint, his Opticks had considerable 
influence on the literary world. English poets, who celebrated the 
discoveries of their country's greatest scientist, and who were dimly 
aware of the significance of Newton's theory of gravity, could not 
grasp the technical details of the geometric axioms and proofs of 
the Principia. But Newton's theory of colors and light provided 
ample opportunity for poetic fancy, as in James Thomson's, "To the 
Memory of Sir Isaac Newton" (1727). 

. . . First the flaming red, 
Springs vivid forth; the tawny orange next; 
And next delicious yellow; by whose side 
Fell the kind beams of all-refreshing green. 
Then the pure blue, that swells autumnal skies, 
Ethereal played; and then, of sadder hue, 
Emerged the deepened indigo, as when 
The heavy-skirted evening droops with frost; 
While the last gleamings of refracted light 
Died in the fainting violet away. 

Leaders of the nineteenth-century Romantic movement in 
literature, and the German "nature philosophers," did not think so 
highly of Newton's theory of color. The scientific procedure of 
dissecting and analyzing natural phenomena by experiments was 
distasteful to them. They preferred to speculate about the unifying 
principles of all natural forces, in the hope of being able to grasp 
nature as a whole. The German philosopher Friedrich Schelling 
wrote in 1802: 

Newton's Opticks is the greatest illustration of a 
whole structure of fallacies which, in all its parts, is 
founded on observation and experiment. 



SG 13.16 



OPTICKS^ 

O R, A 

TREATISE 

OF THE 

REFLEXIONS, REFRACTIONS 
INFLEXIONS and COLOURS 

LIGHT. 

ALSO 

Two TREATISES 

OF THE 

SPECIES and MAGNITUDE 

OP 

Curvilinear Figures; 



LONDON, 
Printed for SviM. Smith, and Ben). Wal»oiid, 
Printeci to the Royal S ociety, at the Pnmt'i Jrmi 
St. ?tuC-i Church.yard. MDCCIV. 



Title page from the first edition of 
Newton's Opticks (1704), in wiiich he 
described his theory of light. 



SG 13.17 



20 



Light 



To the nineteenth-century physicists 
who were trying to use Newton's 
theory to explain newly-discovered 
color phenomena, Goethe addressed 
the following poem: 

May ye chop the light in pieces 
Till it hue on hue releases; 
May ye other pranks deliver, 
Polarize the tiny sliver 
Till the listener, overtaken. 
Feels his senses numbed and 

and shaken- 
Nay, persuade us shall ye never 
Nor aside us shoulder ever. 
Steadfast was our dedication — 
We shall win the consummation. 



SG 13.18, 13.19 



The German poet Goethe (mentioned in Chapter 1 1 in con- 
nection with Nature Philosophy) spent many years on a work 
intending to overthrow Newton's theoi-y of colors, both by his own 
observations and by impassioned arguments. Goethe insisted on the 
purity of white hght in its natural state. He rejected Newton's 
hypothesis that white Hght is a mixture of colors and suggested 
that colors are produced by the interaction of white light and its 
opposite, darkness. Although Goethe's observations on color 
perception were of some value to science, his theory of the physical 
nature of color could not survive scrutiny based on detailed 
experiment. Newton's theory of color remained firmly established, 
even in literature. 

Q9 How did Newton show that white light was not "pure"? 

Q10 Why could Newton be confident that, say, green light was 
not itself composed of different colors of light? 

Q11 How would Newton explain the color of a blue shirt? 

Q12 Why was Newton's theory of color attacked by the nature 
philosophers? 



The Angstrom unit is named after 
Anders Jonas Xngstrom, a Swedish 
astronomer who, in 1862, used 
spectroscopic techniques to detect 
the presence of hydrogen in the sun. 



The amount of scattering of different 
waves by a tiny obstacle Is Indicated 
here for three wavelengths. 



13.6 Why is the sky blue? 

Newton suggested that the apparent colors of natural objects 
depend on which color is predominantly reflected or scattered to the 
viewer by the object. In general, there is no simple way of predicting 
from the surface structure and chemical composition, etc., what 
colors a solid or liquid will reflect or scatter. However, the blue 
color of the clear sky can be understood by a fairly simple argument. 

As Thomas Young found (Sec. 13.4), different wavelengths of 
light correspond to different colors. The wavelength of hght may be 
specified in units of Angstrom (A), equal to lO"'" meter; the range 
of the spectrum visible to humans is from about 7000 A for red 
hght to about 4000 A for violet light. 

Small obstacles can scatter the energy of an incident wave in 
aU directions, and the amount of scattering depends on the wave- 
length. This fact can be demonstrated by experiments with water 
waves in a ripple tank. As a general rule, the longer a wave is 
compared to the size of the obstacle, the less it is scattered by the 
obstacle. For particles smaller than one wavelength, the amount of 




m))i] 






1 1 



11 



in-,:;,-.' 'Ill 



Section 13.7 



21 



scattering of light varies inversely with the fourih power of the 
wavelength. This means that, since the wavelength of red light is 
about twice the wavelength of blue light, the scattering of red hght 
is about l/16th as much as the scattering of blue hght. 

Now we can understand why the sky is blue. Light from the 
sun is scattered by air molecules and particles of dust in the sky. 
These particles are usually very small compared to the wavelengths 
of visible light, so light of short wavelengths -blue light -will be 
much more strongly scattered from the particles than hght of 
longer wavelengths. When you look up into a clear sky, it is mainly 
this scattered light that enters your eye. The range of scattered 
short wavelengths (and the color sensitivity of the human eye) lead 
to the sensation of blue. If you look directly at the sun at sunset 
on a very hazy day, you receive hght of longer wavelengths that has 
not been scattered out -so you perceive the sun as reddish. 

If the earth had no atmosphere, the sky would appear black 
and stars would be visible by day. In fact, starting at altitudes of 
about ten miles, where the atmosphere becomes quite thin, the 
sky does look black and stars can be seen during the day, as has 
been reported by astronauts. 

When the air contains dust particles or water droplets as large 
as the wavelength of visible light (about 10 '■ meter), other colors 
than blue may be strongly scattered. For example, the quality of sky 
coloring changes with the water-vapor content of the atmosphere. 
On clear, dry days the sky is a much deeper blue than on clear days 
with high humidity. The intensely blue skies of Italy and Greece, 
which have been an inspiration to poets and painters for centuries, 
are a result of exceptionally dry air. 



Q13 How does the scattering of hght waves by tiny obstacles 
depend on the wavelength? 

Q14 How would you explain the blue color of the earth's sky? 
What do you expect the sky to look hke on the moon? Why? 



13.7 Polarization 

Newton could not accept the proposal of Hooke and Huygens 
that light is in many ways hke sound -that is, that hght is a wave 
propagated through a medium. Newton argued that hght must also 
have some particle-hke properties. He noted two properties of light 
that, he thought, could not be explained without thinking of light 
as having particle properties. First, a beam of hght is propagated 
in straight lines, whereas waves such as sound spread out in all 
directions and go around corners. The answer to this objection 
could not be given until early in the nineteenth century, when 
Young was able to measure the wavelength of hght and found it to 
be exceedingly small. Even red light, which has the longest wave- 
length of the visible spectrum, has a wavelength less than a 
thousandth of a milhmeter. As long as a beam of hght shines on 
objects or through holes of ordinary size (a few mUhmeters or more 




An observer looking at a sunset on a 
hazy day is receiving primarily un- 
scattered colors such as red; whereas 
if the observer looks overhead, he will 
be receiving primarily scattered colors, 
the most dominant of which is blue. 



If light is scattered by particles 
considerably larger than one wave- 
length (such as the water droplets 
in a cloud), there isn't a very large 
difference in the scattering of 
different wavelengths, so we receive 
the mixture we perceive as white. 



22 



Light 




Iceland Spar Crystal 
Doublo Refraction 




Do^ <it: 




Double refraction by a crystal of Ice- 
land spar. The "unpolarized" incident 
ight can be thought of as consisting 
of two polarized components. The 
crystal separates these two compo- 
nents, transmitting them through the 
crystal in different directions and with 
different speeds. 



in width), the Ught will appear to travel in straight lines. Diffraction 
and scattering effects don't become evident until a wave strikes an 
object whose size is about equal to or smaller than the wavelength. 

Newton's second objection was based on the phenomenon of 
"polarization" of light. In 1669, the Danish scientist Erasmus 
Bartholinus discovered that crystals of Iceland spar (calcite) had 
the curious property of splitting a ray of light into two rays. Thus 
small objects viewed through the crystal looked double. 

Newton thought this behavior could be explained by assuming 
that the ray of light is a stream of particles that have different 
"sides" — for example, rectangular cross-sections. The double 
images, he thought, represent a sorting out of light particles which 
had entered the medium with different orientations. 

Around 1820, Young and Fresnel gave a far more satisfactory 
explanation of polarization, using a modified wave theory of light. 
Before then, scientists had generally assumed that light waves, like 
sound waves, must be longitudinal. (And, as Newton believed, 
longitudinal waves could not have any directional property.) Young 
and Fresnel showed that if light waves are transverse, this would 
account for the phenomenon of polarization. 




A. unpolarized wave on a rope 



!M\ 



B. polarized wave on a rope 

In Chapter 12, we stated that in a transverse wave, the motion 
of the medium itself is always perpendicular to the direction of 
propagation of the wave. That does not mean that the motion of the 
medium is always in the same direction; it could be in any direction 
in a plane perpendicular to the direction of propagation. However, 
if the motion of the medium is predominantly in one direction, for 
example, vertical, we say that the wave is polarized. (Thus a 
polarized wave is really the simplest kind of transverse wave; an 
unpolarized transverse wave is a more complicated thing, since it is 
a mixture of various transverse motions.) The way in which Iceland 
spar (a crystalline form of calcium nitrate) separates an unpolarized 
light beam into two polarized beams is sketched in the margin. 

Scientific studies of polarization continued throughout the 
nineteenth century, but practical applications were frustrated 
because polarizing substances like Iceland spar were scarce and 
fragile. One of the best polarizers was "herapathite." or sulfate of 
iodo-quinine, a synthetic crystalline material. The needle-like 
crystals of herapathite absorb light which is polarized in the 
direction of the long crystal axis; the crystals absorb very little of 
the light polarized in a direction at 90° to the long axis. The crystals 
were so fragile that there seemed to be no way of using them. 



Section 13.7 



23 



But in 1928, Edwin H. Land, while still a freshman student at 
college, invented a polarizing plastic sheet he called "Polaroid." 
His first polarizer consisted of a plastic film in which many micro- 
scopic crystals of herapathite were imbedded. When the plastic is 
stretched, the needle-Uke crystals hne up in one direction, so that 
they all act on incoming hght in the same way. 

Some properties of a polarizing material are easily demonstrated. 
Hold a polarizing sheet -for example, the lens of a pair of polar- 
izing sunglasses -in front of a light source and look at it through 
another polarizing sheet. Rotate the first sheet. You will notice 
that, as you do so, the light alternately brightens and dims; you 
must rotate the second sheet through an angle of 90° to go from 
maximum brightness to maximum dimness. 

How can this be explained? If the light that strikes the first 
sheet is originally unpolarized-that is, a mixture of waves 
polarized in various directions -then the first sheet will transmit 
those waves that are polarized in one direction, and absorb the 
rest, so that the transmitted wave going toward the second sheet 
will be polarized in one direction. Whenever this direction happens 
to coincide with the direction of the long molecules in the second 
sheet, then the wave will be absorbed by the second sheet because 
it will set up vibrations within the molecules and lose most of its 
energy in this way. However, if the direction is perpendicular to 
the long axis of the molecules, the polarized light will go through 
the second sheet without much absorption. 

Interference and diffraction effects required a wave model for 
hght. To explain polarization phenomena, the wave model was 
made more specific by showing that hght could be explained 
by transverse waves. This model for hght explains well all the 
characteristics of hght considered so far-but we shall see in Unit 
5 that it turned out, nevertheless, to require further extension. 



Q1 5 What two objections did Newton have to a wave model ? 

Q16 What phenomena have we discussed that are consistent 
with a wave model of light? 

Q17 Have we proved that light can have no particle 
properties? 



Later, Land improved Polaroid by 
using polymeric molecules com- 
posed mainly of iodine in place of 
the herapathite crystals. 



The eyes of bees and ants are 
sensitive to the polarization of 
scattered light from the clear sky, 
enabling a bee to navigate by the 
sun, even w^hen the sun is low on 
the horizon or obscured. Following 
the bee's example, engineers have 
equipped airplanes with polarization 
indicators for use in arctic regions. 
(See Reader 4 article, "Popular 
Applications of Polarized Light") 

SG 13.20, 13.21 



13.8 The ether 

One thing seems clearly to be missing from the wave model 
for hght. In Chapter 12, we discussed waves as a disturbance that 
propagates in some substance or "medium," such as a rope or 
water. What is the medium for the propagation of hght waves? 

Is air the medium for hght waves? No, because light can pass 
through airless space -for example, the space between the sun or 
other stars and the earth. Even before it was definitely known that 
there is no air between the sun and the earth, Robert Boyle had 
tried the experiment of pumping almost all of the air out of a glass 
container and found that objects inside remained visible. 



24 



Light 



•Ether" was originally the name 
for Aristotle's fifth element, the 
pure transparent fluid that filled the 
heavenly sphere; it was later called 
■quintessence" (see Sections 2.1 
and 6.4). 



In order to transmit transverse 
waves, the medium must have some 
tendency to return to Its original 
shape when it has been deformed 
by a transverse pulse. As Thomas 
Young remarked, "This hypothesis 
of Mr. Fresnel is at least very 
ingenious, and may lead us to some 
satisfactory computations; but it is 
attended by one circumstance which 
is perfectly appalling in its con- 
sequences . . It is only to solids 
that such a lateral resistance has 
ever been attributed: so that ... it 
might be inferred that the luminif- 
erous ether, pervading all space, 
and penetrating almost all sub- 
stances, is not only highly elastic, 
but absolutely solid!!! ' 



Since it was difficult to think of a disturbance without specify- 
ing what was being disturbed, it was natural to propose that a 
medium for the propagation of light waves existed. This medium 
was called the ether. 

In the seventeenth and eighteenth centuries the ether was 
imagined to be an invisible fluid of very low density, which could 
penetrate all matter and fill all space. It might somehow be asso- 
ciated with the "effluvium" (something that "flows out") that was 
imagined to explain magnetic and electric forces. But light waves 
must be transverse in order to explain polarization, and usually 
transverse waves propagate only in a solid medium. A liquid or a 
gas cannot transmit transverse waves for any significant distance, 
for the same reason that you cannot "twist" a liquid or a gas. So 
nineteenth-century physicists assumed that the ether must be 
a solid. 

As was stated in Chapter 12, the speed of propagation increases 
with the stiffness of the medium, and decreases with its density. 
Therefore, the ether was thought to be a ver\' stiff solid with a very 
low density because the speed of propagation is veiT high, com- 
pared to other kinds of waves such as sound. 

Yet, it seems absurd to say that a stiff, solid ether fills all space. 
We know that the planets move without slowing down, so apparent- 
ly they encounter no resistance from a stiff ether. And, of course, we 
ourselves feel also no resistance when we move around in a space 
that transmits light freely. 

Without ether, the wave-theory seemed improbable. But the 
ether itself had absurd properties. Until early in this century, this 
was an unsolved problem, just as it was for Newton and the poet 
Richard Glover who wrote, shortly after Newton's death: 

O had great Newton, as he found the cause 

By which sound rouls thro" th" undulating air, 

O had he, baffling time's resistless power, 

Discover'd what that subtile spirit is. 

Or whatsoe'er diffusive else is spread 

Over the wide-extended universe. 

Which causes bodies to reflect the light. 

And from their straight direction to divert 

The rapid beams, that through their surface pierce. 

But since embracd by th' icy arms of age. 

And his quick thought by times cold hand congeal'd. 

Ev'n NEWTON left unknown this hidden power .... 



We shall see how. following Einstein's modification of the theory 
of light, the problem came to be solved. 

Q18 Why was it assumed that an "ether" existed which 
transmitted light waves? 

Q19 What remarkable property must the ether have if it is 
to be the mechanical medium for the propagation of light? 



''^^i-.v.^ 



^.^^i^i^SSk. 



..d5v!v^. 




J 



"Entrance to the Harbor", a painting by Georges Seurat (1888). Art historians believe 
that Seurat's techniques of pointillism, the use of tiny dots of pure color to achieve all 
effects in a painting, reflects his understanding of the physical nature of light. 



13 1 The Project Physics learning materials 
particularly appropriate for Chapter 13 include: 
Experiments 
Refraction of a Light Beam 
Young's Experiment — the Wavelength of Light 
Activities 
Thin Film Interference 
Handkerchief Diffraction Grating 
Photographing Diffraction Patterns 
Poisson"s Spot 
Photographing Activities 
Color 

Polarized Light 
Making an Ice Lens 
Reader Articles 
Experiments and Calculations Relative to 

Physical Optics 
Velocity of Light 

Popular Applications of Polarized Light 
Eye and Camera 
Lenses and Optical Instruments 
In addition the following Project Physics 
materials can be used with Unit 4 in general: 
Reader Articles 
Action at a Distance 
Maxwells Letters: A Collection 
Film 
People and Particles 

13.2 A square card. 3 cm on a side, is held 10 cm 
from a small penlight bulb, and its shadow falls 
on a wall 15 cm behind the card. What is the 
size of the shadow on the wall? (A diagram of the 
situation will be useful.) 

13.3 The row of photographs on page 9 shows 
what happens to a beam of light that passes 
through a narrow slit. The row of photographs on 
page 126 of Chapter 12 shows what happens to a 
train of water wave that passes through a narrow 
opening. Both sets of photographs illustrate single- 
slit diffraction, but the photographs are not at all 
similar in appearance. Explain the difference in 
appearance of the photographs, and how they are 
similar. 

13.4 An experiment to determine whether or not 
the propagation of light is instantaneous is 
described by Galileo as follows: 

Let each of two persons take a light contained 
in a lantern, or other receptacle, such that by 
the interposition of the hand, the one can shut 
off or admit the light to the vision of the other. 
Next let them stand opposite each other at a 
distance of a few cubits and practice until 
they acquire such skill in uncovering and 
occulting their lights that the instant one 
sees the light of his companion he will 
uncover his own. After a few trials the 
response will be so prompt that without 
sensible error (svario) the uncovering of one 
light is immediately followed by the uncover- 
ing of the other, so that as soon as one exposes 
his light he will instantly see that of the other. 
Having acquired skill at this short distance let 
the two experimenters, equipped as before 



take up positions separated by a distance of 
two or three miles and let them perform the 
same experiment at night, noting carefully 
whether the exposures and occultations occur 
in the same manner as at short distances; if 
they do. we may safely conclude that the 
propagation of light is instantaneous but if 
time is required at a distance of three miles 
which, considering the going of one light and 
the coming of the other, really amounts to six. 
then the delay ought to be easily observable . . . . 

But later he states: 

In fact I have tried the experiment only at a 
short distance, less than a mile, from which 
I have not been able to ascertain with certainty 
whether the appearance of the opposite light 
was instantaneous or not; but if not instanta- 
neous, it is extraordinarily rapid .... 

(a) Why was GaUleo unsuccessful in the above 
experiment? 

(b) How would the experiment have to be 
altered to be successful? 

(c) What do you think is the longest time that 
light might have taken in getting from one 
observer to the other without the observers 
detecting the delay? Use this estimate to 
arrive at a lower limit for the speed of light 
that is consistent with Galileo's description 
of the result. 

(d) Why do you suppose that the first proof of 
the finite speed of light was based on 
celestial observations rather than terrestrial 
observations? 

13.5 A convenient unit for measuring astronomi- 
cal distances is the light year, defined to be the 
distance that light travels in one year. Calculate 
the number of meters in a Ught year to two 
significant figures. 

13.6 What time would be required for a space- 
ship having a speed of 1 1000 that of light to 
travel the 4.3 light years from the earth to the 
closest known star other than the sun. Proxima 
Centauri? Compare the speed given for the 
spaceship with the speed of approximately 10 km 
sec maximum speed (relative to the earth) that a 
space capsule has on an earth-moon trip. 

13.7 Newton supposed that the reflection of light 
off shiny surfaces is due to "some feature of the 
body which is evenly diffused over its surface and 
by which it acts upon the ray without contact." 
The simplest model for such a feature would be 

a repulsi\'e force which acts only in a direction 
perpendicular to the surface. In this question you 
are to show how this model predicts that the 
angles of incidence and reflection must be equal. 
Proceed as follows: 
(a) Draw a clear diagram showing the in- 
cident and reflected rays. Also show the 
angles of incidence and reflection {6, and 
Oj). Sketch a coordinate system on your 
diagram that has an x-axis parallel to the 
surface and a y-axis perpendicular to the 



26 



surface. Note that the angles of incidence 
and reflection are defined to be the angles 
between the incident and reflected rays 
and the y-axis. 

(b) Supposing that the incident light consists 
of particles of mass m and speed v. what 
is the kinetic energy of a single particle? 
Write mathematical expressions for the x 
and y components of the momentum of an 
incident light particle. 

(c) If the repulsive force due to the reflect- 
ing surface does no work on the particle 
and acts only perpendicular to the 
surface, which of the quantities that 
you have described in part (b) is 
conserved? 

(d) Show algebraically that the speed u of the 
reflected particle is the same as the speed 
V of the incident particle. 

(e) Write mathematical expressions for the 
components of the momentum of the 
reflected particle. 

(f) Show algebraically that d, and O2 must be 
equal angles. 

13.8 Find the shortest path from point A to any 
point on the surface M and then to point B; Solve 
this by trial and error, perhaps by experimenting 
with a short piece of string held at one end by a 
tack at point A. (A possible path is shown but it 
is not necessarily the shortest one.) Notice that 
the shortest distance between A, M and B is also 
the least-time path for a particle traveling at a 
constant speed from A to M to B. What path would 
light take from A to M to B? Can you make a 
statement of the law of reflection in terms of this 
principle instead of in terms of angles? 




Draw clear straight-line diagrams to show how a 
pair of diverging rays can be used to help explain 
the following phenomena. 

(a) The mirror image of an object appears to 
be just as far behind the mirror as the 
object is in front of the mirror. 

(b) A pond appears shallower than it actually is. 

(c) A coin placed in an empty coffee mug 
which is placed so that the coin cannot 
quite be seen becomes visible if the mug 
is filled with water. 

13.12 Due to atmospheric refraction we see the 
sun in the evening for some minutes after it is 
really below the horizon, and also for some 
minutes before it is actually above the horizon 
in the morning. 

(a) Draw a simple diagram to illustrate how 
this phenomenon occurs. 

(b) What would sunset be like on a planet with 
a very thick and dense (but still transparent) 
atmosphere? 

13.13 In a particle theory of light, refraction 
could be explained by assuming that the particle 
was accelerated by an attractive force as it passed 
from air or vacuum toward a medium such as 
glass. Assume that this accelerating force could 
act on the particle only in a direction perpendicular 
to the surface, and use vector diagrams to show 
that the speed of the particle in the glass would 
have to be greater than in air. 



^rttt. 



^c*"- 

i 



X 



iv^.^.^ r 



'M. 



13.9 What is the shortest mirror in which a 6-foot- 
tall man can see himself entirely? (Assume that 
both he and the mirror are vertical and that he 
places the mirror in the most favorable position.) 
Does it matter how far away he is from the 
mirror? Do your answers to these questions 
depend on the distance from his eyes to the top 

of his head? 

13.10 Suppose the reflecting surfaces of every 
visible object were somehow altered so that they 
completely absorbed any light falling on them; 
how would the world then appear to you? 

13.11 Objects are visible as a whole if their 
surfaces reflect light enabling our eyes to intercept 
cones of reflected light diverging from each part 
of the surface. The accompanying diagram shows 
such a cone of light (represented by 2 diverging 
rays) entering the eye from a book. 



13.14 Plane parallel waves of single-wavelength 
light illuminate the two narrow slits, resulting in 
an interference pattern of alternate bright and 
dark fringes being formed on the screen. The 
bright fringes represent zones of constructive 




•PArv pirfijseiJte, 



interference and hence appear at a point such as 
P on the diagram above only if the diffracted 
waves from the two slits arrive at P in phase. 
The diffracted waves will only be in phase at 
point P if the path difference is a whole number 
of wavelengths (that is, only if the path difference 
equals mX where m = 0, 1, 2, 3 . . . ). 



27 




■ f<w j>i>^i=teeiKe- 



(a) What path difference resuhs in destructive 
interference at the screen? 

(b) The separation between two successive 
bright fringes depends on the wavelengths 
of the Hght used. Would the separation be 
greater for red hght or for blue Ught? 

(c) For a particular color of hght. how would 
the pattern change if the distance of the 
screen from the shts is increased? (Hint: 
make two diagrams.) 

(d) What changes occur in the pattern if the 
slits are moved closer together? (Hint: 
make two diagrams.) 

(e) What happens to the pattern if the shts 
themselves are made more narrow? 

13.15 Recalling diffraction and interference 
phenomena from Chapter 12. show that the wave 
theory- of hght can be used to explain the bright 
spot that can be found in the center of the shadow 
of a disk illuminated by a point source. 







13.16 It is now a familiar observation that 
clothing of certain colors appears different 
in artificial light and in sunlight. 
Explain why. 

13.17 .Another poem by James Thomson (1728): 

Meantime, refracted from yon eastern cloud. 
Bestriding earth, the grand ethereal bow 
Shoots up immense: and every hue unfold. 
In fair proportion running from the red 
To where the violet fades into the skv. 



Here, awe-ful Newton, the dissolving clouds 
Form, fronting on the sun. thy shower>- prism; 
And to the sage-instructed eye unfold 
The various twine of hght. by thee disclosed 
From the white minghng blaze. 

How do you think it compares with the poem on 
p. 20 (a) as poetrv? (b) as physics? 

13.18 Green hght has a wavelength of approxi- 
mately 5 X 10"' meters. WTiat frequency 
corresponds to this wavelength? Compare this 
frequency to the carrier frequency of the radio 
waves broadcast by a radio station vou hsten 
to. (Hint: i^ = f .) 

13.19 The arts sometimes reflect contemporary 
ideas in science; the following poem is an excel- 
lent example of this. 

Some range the colours as they parted fly. 
Clear-pointed to the philosophic eye; 
The flaming red. that pains the dwelling gaze. 
The stainless, lightsome yellow's gilding rays: 
The clouded orange, that betwixt them glows. 
And to kind mixture tawny lustre owers; 
All-chearing green, that gives the spring its dye: 
The bright transparent blue, that robes the sky; 
And indigo, which shaded light displays. 
And violet, which in the view decays. 
Parental hues, whence others all proceed; 
An ever-mingling, changeful, countless breed. 
Unravel'd. variegated, lines of light. 
When blended, dazzling in promiscuous white. 
[Richard Savage (1697-1743). The V^andererX 

(a) Would you or would you not classify the 
poet Richard Savage as a 'nature 
philosopher"? WTiy? 

(b) Compare this poem with the one in SG 13.17 
by James Thomson; which poef do you 
think displayed the better understanding of 
physics of his time? Which poem do you 
prefer? 

13.20 One way to achieve privacy in apartments 
facing each other across a narrow courtyard while 
still allowing residents to enjoy the view of the 
courtyard and the sky above the courtyard is to 
use polarizing sheets placed over the windows. 
Explain how the sheets must be oriented for 
maximum effectiveness. 

13.21 To prevent car drivers from being blinded 
by the lights of approaching autos. polarizing 
sheets could be placed over the headlights and 

w indshields of even- car. Explain why these 
sheets would have to be oriented the same way 
on every vehicle and must have their polarizing 
axis at 45° to the vertical. 



Diffraction fringes around a razor 
blade. 



28 



14.1 Introduction 31 

14.2 The curious properties of lodestone and amber: 32 

Gilbert's De Magnete 

14.3 Electric charges and electric forces 35 

14.4 Forces and fields 42 

14.5 The smallest charge 50 

14.6 Early research on electric charges 51 

14.7 Electric currents 53 

14.8 Electric potential difference 55 

14.9 Electric potential difference and current 58 

14.10 Electric potential difference and power 59 

14.11 Currents act on magnets 60 

14.12 Currents act on currents 62 

14.13 Magnetic fields and moving charges 66 




CHAPTER FOURTEEN 



Electric and Magnetic Fields 



14.1 Introduction 



The subject "electricity and magnetism" makes up a large 
part of modern physics and has important connections with SG 14.1 

almost all other areas of physics and chemistry. Because it would 
be impossible to study this subject comprehensively in the time 
available in an introductory course, we consider only a few main 
topics that will be needed as a foundation for later chapters. Major 
applications of the information in this chapter will appear later: 
the development of electrical technology (Chapter 15), the study of 
the nature of hght and electromagnetic waves ,Chapter 16.. and the 
study of properties of atomic and subatomic particles (Units 5 
and 6). 

In this chapter we shall first treat electric charges and the 
forces between them -very briefly, because the best way to learn 
about that subject is not by reading but by doing experiments in 
the laboratory (see Experiment 33 in the Handbook). Next, we will 
show how the idea of a "field" simplifies the description of electric 
and magnetic effects. Then we will take up electric currents, which 
are made up of moving charges. By combining the concept of field 
with the idea of potential energy we will be able to establish 
quantitative relations between current, voltage, and power. These 
relations will be needed for the practical applications to be 
discussed in Chapter 15. 

Finally, at the end of this chapter, we shall come to the 
relations between electricity and magnetism, a relation having 
important consequences both for technology and basic physical 
theory. We will begin by looking at a simple physical phenomenon: 
the interaction between moving charges and magnetic fields. 

An inside view of "Hilac" (heavy ion linear acceler- 
ator) at Berkeley, California. In this device electric 
fields accelerate charged atoms to high energies. 

31 



32 



Electric and Magnetic Fields 



14.2 The curious properties of lodestone and amber: Gilbert's 
De Magnete 



Lucretius was one of the early 
writers on atomic theorv: see the 
Prologue to Unit 5. 



Two natural substances, amber and lodestone, have aroused 
interest since ancient times. Amber is sap that long ago oozed from 
certain softwood trees, such as pine, and, over many centuries, 
hardened into a semitransparent solid ranging in color from yellow 
to brown. It is a handsome ornamental stone when polished, and it 
sometimes contains the remains of insects that were caught in the 
sticky sap. Ancient Greeks recognized a curious property of amber: 
if rubbed vigorously against cloth, it can attract nearby objects such 
as bits of straw or grain seeds. 

Lodestone is a mineral that also has unusual properties. It 
attracts iron. Also, when suspended or floated, a piece of lodestone 
always turns to take one particular position — a north-south direction. 
The first known written description of the navigational use of 
lodestone as a compass in Western countries dates from the late 
twelfth century, but its properties were known even earlier in 
China. Today, lodestone would be called magnetized iron ore. 

The histories of lodestone and amber are the early histories of 
magnetism and electricity. The modem developments in these 
subjects began in 1600 with the publication in London of William 
Gilbert's book De Magnete. Gilbert (1544-1603) was an influential 
physician, who served as Queen Elizabeth's chief physician. During 
the last twenty years of his life, he studied what was already known 
of lodestone and amber, made his own experiments to check the 
reports of other writers, and summarized his conclusion in De 
Magnete. The book is a classic in scientific literature, primarily 
because it was a thorough and largely successful attempt to test 
complex speculation by means of detailed experiments. 

Gilbert's first task in his book was to review and criticize what 
had previously been written about lodestone. Gilbert reports various 
theories proposed to explain the cause of magnetic attraction; one 
of the most popular theories was suggested by the Roman author 
Lucretius: 

Lucretius . . . deems the attraction to be due to this, that 
as there is from all things a flowing out ("efflux" or 
effluvium") of minutest bodies, so there is from iron an 
efflux of atoms into the space between the iron and the 
lodestone -a space emptied of air by the lodestone's 
atoms (seeds); and when these begin to return to the 
lodestone, the iron follows, the corpuscles being en- 
tangled with each other. 

Gilbert himself did not accept the effluvium theory as an explanation 
for magnetic attraction, although he thought it might apply to 
electrical attraction. 

When it was discovered that lodestones and magnetized needles 
or bars of iron tend to turn so as to have a certain direction on the 
surface of the earth, many authors proposed explanations. But, 
says Gilbert, 



Some quotations and diagrams 
from Gilbert's Oe Magnate. 



TraSatuStftvc Phyfuuogia Nova 

M AGNET E, 

Magneticifqjcorporibus & magno 

Magnetc tcllurc, fcx Iibris comprchcnfus. 

aGulLlELMO G5LBEXTO CoJcC" 

ftrenfi. Medico Londinenli. 

In tj$iihus M, qm ad banc matcriamJJ>effant,plurimu 

y Arpmeniu isf experimcntis exfJhjTme abjoktifi. 
me^ trdlantw y cxpHoKtur. 

Omnia nunc diligcncer recognita,& craendatius quam ante 
in lucem ediu , auiia & figuns lUuftrita , opera Sc ftudio D . 

WOIFCANCI LoCHMANS, I. U. D. 

Sc Matbemwci. 

Jidcakemlihria£urilhtt(i Index caphm , Renmi!fVerborm 
hcufUtifsiims, qui inpmre 4<litmcdffidertdMttur. 




S E D J N I , 

Typjs GOTZIANIS 

Akmo M. DC. zxziii. 



The title page of the third edition (1633) of Gilbert's 
book is reproduced above. Early in the book Gilbert 
makes the following statement: 

Before we expound the causes of magnetic 
movements and bring forward our demonstra- 
tions and experiments touching matters that 
for so many ages have lain hid . . . we must 
formulate our new and till now unheard-of 
view of the earth, and submit it to the 
judgment of scholars. 



Gilbert proposed an elaborate analogy between the 
earth and a spherical lodestone. At the right are 
reproduced some of the drawings Gilbert used to 
illustrate his experiments with magnetized needles 
and spheres of iron and lodestone. Toward the end 
of the book, he presents the diagram at the right, 
which shows the angle at which a magnetic needle 
would "dip " toward the earth's surface (represented 
by the central circle) at different latitudes. The section 
of De Magnete in which this diagram appears is 
titled: How to find . . . the latitude of any place by 
means of the following diagram, turned into a 
magnetic instrument, in any part of the world, 
without the help of the heavenly bodies, sun, planets, 
or fixed stars, and in foggy weather as well as in 
darkness. 




34 



Electric and Magnetic Fields 



The immensely important idea of 
"field" was introduced into ptiysics 
by Michael Faraday early in the 
nineteenth century, and developed 
further by Kelvin and Maxwell (see 
Sees. 14.4 and 16.21. 



. . . they wasted oil and labor, because, not being practical 
in the research of objects of nature, being acquainted 
only with books, being led astray by certain erroneous 
physical systems, and having made no magnetical experi- 
ments, they constructed certain explanations on a basis 
of mere opinions, and old-womanishly dreamt the things 
that were not. Marcilius Ficinus chews the cud of ancient 
opinions, and to give the reason of the magnetic direction 
seeks its cause in the constellation Ursa . . . Paracelsus 
declares that there are stars which, gifted with the lode- 
stone's power, do attract to themselves iron . . . All these 
philosophers . . . reckoning among the causes of the 
direction of the magnet, a region of the sky, celestial 
poles, stars . . . mountains, cliffs, vacant space, atoms, 
attractional . . . regions beyond the heavens, and other 
like unproved paradoxes, are world-wide astray from the 
truth and are blindly wandering. 

Gilbert himself proposed the real cause of the lining-up of a 
magnetic needle or lodestone when suspended by itself: the earth 
itself is a lodestone. Gilbert also did a rather ingenious experiment 
to show that his hypothesis was a likely one: he prepared a large 
piece of natural lodestone in the shape of a sphere, and showed 
that a small magnetized needle placed on the surface of such a 
lodestone will act in the same way as a compass needle does at 
different places on the earth's surface. If the directions along which 
the needle lines up are marked with chalk on the lodestone, they 
will form meridian circles (similar to the lines of equal longitude 
on a globe of the earth) which converge at two opposite ends that 
may be called "poles." At the poles, the needle will point perpendic- 
ular to the surface of the lodestone (see p. 33). Halfway between, 
along the "equator," the needles will lie along the surface. Small 
bits of iron wire placed on the surface of the spherical lodestone 
line up along these same directions. 

The discussion of these and other actions of magnets now 
generally uses the idea that magnets set up "fields" all around 
themselves. The field can then act on other objects near or distant. 
Gilbert's description of the force exerted on the needle by his 
spherical lodestone (which he called the "terrella." meaning "little 
earth") was a step toward the modern field concept: 

The terrellas force extends in all directions .... But 
whenever iron or other magnetic body of suitable size 
happens within its sphere of influence it is attracted; yet 
the nearer it is to the lodestone the greater the force with 
which it is borne toward it. 



'electric ' comes from the Greek 
word electron, meaning "amber.' 



Gilbert also included a discussion of electricity in his book. He 
introduced the word electric as the general term for "bodies that 
attract in the same way as amber." Gilbert showed that electric and 
magnetic forces are different. For example, a lodestone always 
attracts iron or other magnetic bodies, whereas an electric object 
exerts its attraction only when it has been recently rubbed. On the 



Section 14.3 35 

other hand, an electric object can attract small pieces of many 
different substances, whereas magnetic forces act only between a 
few types of substances. Objects are attracted to a rubbed electric 
object along lines directed toward one center region, but a magnet 
always has two regions (poles) toward which other magnets are 
attracted. 

In addition to summarizing the then known facts of electricity 
and magnets, Gilbert's work suggested new research problems that 
were pursued by others for many years. For example, Gilbert 
thought that while the poles of two lodestones might either attract 
or repel each other, electric bodies could never exert repulsive 
forces. But in 1646, Sir Thomas Browne published the first account 
of electric repulsion. To systematize such observations a new 
concept, electric charge, was introduced. In the next section we 
will see how this concept can be used to describe the forces 
between electrically charged bodies. 

Q1 How did Gilbert demonstrate that the earth behaves like a 
spherical lodestone? 

Q2 How does the attraction of objects by amber differ from the 
attraction by lodestone? 

14.3 Electric charges and electric forces 

As Gilbert strongly argues, the facts of electrostatics (the effects 
of forces between electric charges at rest) must be learned in the 
laboratory rather than by just reading about them. This section, 
therefore, is only a brief outline to prepare for (or to summarize) 
your own experience with the phenomena. 

The behavior of amber was discussed earlier: when it is rubbed 
it almost mysteriously acquires the property of picking up chaff, 
small bits of cork, paper or hair, etc. To some extent all materials 
show this effect when rubbed, including rods made of glass or hard 
rubber, or strips of plastic. There are two other important sets of 
basic observations: (a) where two rods of the same material have 
been rubbed with the same kind of cloth, the rods repel each other. 
Examples that were long ago found to work especially well are two 
glass rods rubbed with silk, or two hard rubber rods rubbed with 
fur; (b) but when two rods of different material have been rubbed - 
for example, a glass rod rubbed with silk, and a rubber rod rubbed 
with fur— the two rods may attract each other. 

These and thousands of similar experimentally observable facts 
can be summarized in a systematic way by adopting a very simple 
model. Remember that the model we have been describing is not an 
experimental fact which you can observe separately. It is, rather, 
a set of invented ideas which help us describe and summarize what 
we can see happening. It is easy to forget this important difference 
between experimentally observable fact and invented explanations. 
Both are needed, but they are not the same thing! The model 
consists of the concept of "charge" and three rules. An object that 



36 



Electric and Magnetic Fields 




Benjamin Franklin (1706-1790), Amer- 
ican statesman, inventor, scientist, 
and writer. He was greatly interested 
in the phenomena of electricity: his 
famous kite experiment and invention 
of the lightning rod gained him wide 
recognition. He is shown here observ- 
ing the behavior of a bell whose clap- 
per is connected to a lightning rod. 



has been rubbed and acquired the property of attracting small bits 
of stuff is said to "be electrically charged"" or to "have an electric 
charge."" Further, we imagine that there are two kinds of charge, 
so that all objects showing electrical behavior have either one or 
the other of the two kinds of charge. The three rules are: 

(1) There are only two kinds of electric charge. 

(2) Two objects charged alike (that is, having the same kind of 
charge) repel each other. 

(3) Two objects charged oppositely attract each other. 
Another basic observation is that when two different uncharged 

materials are rubbed together (for example, the glass rod and the 
silk cloth) they will acquire opposite kinds of charge. Benjamin 
Franklin, who did many experiments with electric charges, proposed 
a mechanical model that would account for all these phenomena. 
In his model, charging an object electrically involved the transfer 
of an "electric fluid"" that was present in all matter. When two 
objects were rubbed together, some electric fluid from one passed 
into the other; the one body would then have an extra amount of 
fluid and the other a lack of fluid. An excess of fluid produced one 
kind of electric charge -which Franklin called "positive." A lack 
of the same fluid produced the other kind of electric charge -which 
he called "negative." 

Previously "two-fluid"" models had been proposed, which 
involved both a "positive fluid"" and a "negative fluid""; in normal 
matter, these two fluids were thought to be present in equal 
amounts that cancelled out each other"s eff'ects. When two different 
objects were rubbed together, there would be a transfer of fluids 
that would leave one with an unbalanced amount of positive fluid 
and the other with an unbalanced amount of negative fluid. 

There was some dispute between advocates of one-fluid and 
two-fluid models, but nevertheless there was agreement to speak 
of the two kinds of electrical condition a charged body could be in 
as "+'" or "— ." It was not until the late 1890"s that there was 
experimental evidence to give convincing support to any model of 
what "electric charge" actually was. There were, as it turned out, 
elements of truth in both one-fluid and two-fluid models. The stor\' 
will be told in some detail in Unit 5. For the present, we can say 
that there are in fact two different material "fluids,"" but the 
"negative fluid"" moves around much more easily than the "positive 
fluid,"' so most of the electric phenomena we have been discussing 
were in fact due to an excess or deficiency of the mobile fluid. 

Franklin thought of the electric fluid as consisting of tiny 
particles, and that is the present view. too. Consequently, the word 
charge is commonly used as a plural, for example, in the statement 
"electric charges transfer from one body to another.'" 

What is amazing in electricity, and indeed in other parts of 
physics, is that so few concepts are needed to deal with an in- 
finitude of different observations. For example, it turns out we do 
not need to invent a third or fourth kind of charge in addition to 
"+" and "— ." No observation of charged objects requires some 



Section 14.3 



37 



additional type of charge that might have to be called "-^" or "x." 

Even the behavior of an uncharged body can be understood in 
terms of + amd — charges. Any piece of matter large enough to be 
visible can be considered to contain a large amount of electric 
charge, both positive and negative. If the amount of positive charge 
is equal to the amount of negative charge, this piece of matter will 
appear to have no charge at all (that is to say, zero charge). So we 
can say that the effects of the positive and negative charges simply 
cancel each other when they are added together. (This is one 
advantage of calling the two kinds of charge positive and negative, 
rather than, for example, x and y.) When we talk about the electric 
charge on an object we usually mean the slight excess (or net) 
charge of either positive or negative charge existing on this object. 



The electric force law. What is the "law of force" between 
electric charges? In other words, how does the force depend on the 
amount o/ charge, and on the distance between the charged objects? 

The first evidence of the nature of the force law between 
electrical charges was obtained in an indirect way. About 1775, 
Benjamin Franklin noted that a small cork hanging near the outside 
of an electrically charged metal can is strongly attracted; but when 
he lowered the cork, suspended by a silk thread, into the can, he 
found that no electric force was experienced by the cork no matter 
what its position was inside the can. 

Franklin did not understand why the walls of the can did not 
attract the cork when it was inside, whereas they did when it was 
outside. He asked his friend Joseph Priestley to repeat the experiment. 

Priestley verified Franklin's results, and went on to make a 
brilliant inference from them. He remembered from Newton's 
Principia that Newton had proved that gravitational forces behave 
in a similar way. Inside a hollow planet, the net gravitational force 
on an object, obtained by adding up all the forces exerted by the 
parts of the planet, would be exactly zero. This is a result which can 
be deduced mathematically from the law that the gravitational 
force between any two individual pieces of matter is inversely 
proportional to the square of the distance between them. Priestley 
therefore proposed that electrical forces exerted by charges vary 
inversely as the square of the distance, just as do gravitational 
forces exerted by massive bodies. (Zero force inside a hollow 
conductor is discussed on p. 40.) 

Priestley's proposal was based on bold reasoning by analogy. 
Such reasoning could not by itself prove that electrical forces are 
inversely proportional to the square of the distance between charges. 
But it strongly encouraged other physicists to test such an 
hypothesis by experiment. 

The French physicist Charles Coulomb provided direct experi- 
mental confirmation of the inverse-square law for electric charges 
that Priestley had suggested. Coulomb used a torsion balance 
which he had invented. A diagram of the balance is shown on the 
following page. A horizontal, balanced insulating rod is shown 



Our experience with Newton's law 
of gravitation is affecting our 
question. We are assuming that the 
force depends only on a single 
property and on distance. 



Joseph Priestley (1733-1804), a 
Unitarian minister and physical 
scientist, was persecuted in England 
for his radical political ideas. One 
of his books was burned, and a mob 
looted his house because of his 
sympathy with the French Revolu- 
tion. He moved to America, the 
home of Benjamin Franklin, who had 
stimulated Priestley's interest in 
science. Primarily known for his 
identification of the gas oxygen as 
a separate element that is involved 
in combustion and respiration, he 
also experimented in electricity, and 
can claim to be the developer of 
carbonated drinks (soda-pop). 



38 



Electric and Magnetic Fields 



Charles Augustin Coulomb (1738- 
1806) was born into a family of higti 
social position and grew up in an age 
of political unrest. He studied science 
and mathematics and began his career 
as a military engineer. His book The 
Theory of Simple Machines gained 
him membership in the French Acad- 
emy of Sciences. While studying ma- 
chines Coulomb invented his torsion 
balance, with which he carried out in- 
tensive investigations on the mechan- 
ical forces due to electrical charges. 






KJ 




y^ 



'* ''i 




suspended by a thin silver wire, which twists when a force is 
exerted on the end of the rod. The twisting effect could be used to 
measure the force between a charged body A attached to one end 
of the rod and another charged body B placed near it. 

By measuring the twisting effect for different separations 
between the centers of spheres A and B, Coulomb showed that the 
force between charged spheres varied in proportion to 1/R^: 

Thus he directly confirmed the suggestion that the electrical force 
of repulsion for like charges, or attraction for unlike charges, varies 
inversely as the square of the distance between charges. 

Coulomb also demonstrated how the magnitude of the electric 
force depends on their charges. There was not yet any accepted 
method for measuring quantitatively the amount of charge on an 
object (and nothing we have said so far would suggest how to 
measure the magnitude of the charge on a body). Yet Coulomb used 
a clever technique based on symmetry to compare the effects of 
different amounts of charge. He first showed that if a charged 
metal sphere touches an uncharged sphere of the same size, the 
second sphere becomes charged also -we may imagine that during 



Section 14.3 



39 



the moment of contact between the metal objects, some of the 
charge from the first "flows" over, or is "conducted" to, the second. 
Moreover, the two spheres after contact share the original charge 
equally (as demonstrated by the observable fact that they exert 
equal forces on some third, charged test body). In a similar way, 
starting with a given amount of charge on one sphere and sharing 
it by contact among several other identical but uncharged spheres, 
Coulomb could produce charges of one-half, one-quarter, one-eighth, 
etc., of the original amount. By thus varying the charges on the two 
spheres independently, he could show, for example, that when the 
two spheres are both reduced by one-half, the force between the 
spheres is reduced to one-quarter its previous value. In general, he 
found that the magnitude of the electric force is proportional to the 
product of the charges. If we use the symbols q^ and q^ for the net 
charges on bodies A and B, the magnitude Fe\ of the electric force 
that each exerts on the other is proportional to q^ x gg, and may be 
written as Fpi °^ qA<7B- 

Coulomb summarized his results in a single equation which 
describes the electric forces that two small charged spheres A and 
B exert on each other: 

where R is the distance between their centers and fe is a constant 
whose value depends on the units of charge and length that are 
being used. This form of the law of force between two electric 
charges is now called Coulomb's Law. We shall discuss the value 
of k below. For the moment, note the beautiful fact that the 
equation has exactly the same form as Newton's Law of Universal 
Gravitation, though of course it arises from a completely different 
set of observations and applies to a completely different kind of 
phenomenon. Why this should be so is to this day a fascinating 
puzzle, and another token of the basic simplicity of nature. 

The unit of charge. We can use Coulomb's Law to define a unit 
of charge. For example, we could arbitrarily let the magnitude of k 
be exactly 1, and define a unit charge so that two unit charges 
separated by a unit distance exert a unit force on each other. There 
exists a set of units based on this choice. However, in the system 
of electrical units we shall find more convenient to use, the "MKSA" 
system, the unit of charge is derived not from electrostatics but 
from the unit of current, the "ampere." The unit of charge is called 
the "coulomb," and is defined as the amount of charge that flows 
past a point in a wire in one second when the cuiTcnt is equal to 
one ampere. 

The ampere, or "amp," is a familiar unit because it is frequently 
used to describe the current in electrical appliances. The effective 
amount of current in a common 100-watt light bulb is approximately 
one ampere, hence the amount of charge that goes through the 
bulb in one second is about 1 coulomb. So it might seem that the 
coulomb is a fairly small amount of charge. However, one coulomb 



That two equally large spheres 
share the available charge equally 
might have been guessed by what 
is called "argument by symmetry." 
There is no evident reason why the 
charge should not be distributed 
symmetrically, and therefore, divided 
equally among equal spheres. But 
such a guess based on a symmetry 
argument must always be confirmed 
by separate experiment, as it was in 
this case. 



SG 14.2 

The Project Physics documentary 
film People and Particles shows 
an experiment to see if Coulomb's 
law applies to charges at distances 
as small as 10 'cm. (It does.) 



Meter-Kilogram-Second-Ampere 




Consider any point charge P 
inside an even, spherical dis- 
tribution of charges. For any 
small patch of charges with 
total charge Q, on the sphere 
there is a corresponding 
patch on the other side of P 
with total charge Q2. But the 




areas of the patches are 
directly proportional to the 
squares of the distances from 
P. hence the total charges Q, 
and Q2 are also directly pro- 
portional to the squares of 
the distances from P. 
The electric field due to each 




kV<' 



patch of charge is propor- 
tional to the area of the 
patch, and Inversely propor- 
tional to the square of the 
distance from P. So the dis- 
tance and area factors can- 
cel—the forces on P due 
to the two patches at P are 



PX 






exactly equal in magnitude. 
But the forces are also in 
opposite directions. So the 
net force on P is zero owing 
to Q, and Q.,. 

Since this is true for all pairs 
of charge patches, the net 
electric field at P is zero. 



Electric shielding 

In general, charges on a closed conducting 
surface arrange thennselves so that the electric 
force inside is zero just as they do on a sphere 
as shown in the diagrams above. Even if the 
conductor is placed in an electric field, the 
surface charges will rearrange themselves so 
as to keep the net force zero everywhere 
inside. Thus, the region inside any closed 



conductor is "shielded" from any external 
electric field. This is a very important 
practical principle. 

Whenever stray electric fields might disturb 
the operation of some electric equipment, 
the equipment can be enclosed by a shell 
of conducting material. Some uses of 
electric shielding can be seen in the photo- 
graphs of the back of a TV receiver, below. 



Closeup of a tube in the tuning section of the TV 
set on the left. Surrounding the tube is a collapsible 
metal shield. Partly shielded tubes can be seen 
elsewhere in that photo. 




A section of shielded cable such as is 
seen in use in the photo above, show- 
ing how the two wires are surrounded 
by a conducting cylinder woven of 
fine wires. 



Section 14.3 



41 



of net charge all collected by itself in one place is unmanageably 
large! What happens in the light bulb is that each second one 
coulomb of the negative charges that are present in the wires move 
through its filament passing through a more or less stationary 
arrangement of positive charges. The net charge on the filament 
is zero at every moment. 

If the coulomb (1 coul) is adopted as the unit of charge, then 
the constant k in Coulomb's law can be found experimentally, by 
measuring the force between known charges separated by a known 
distance. The value of k turns out to equal about nine billion 
newton-meters squared per coulomb squared ( 9 X 10** Nm^/couP). 
This means that two objects, each with a net charge of one 
coulomb, separated by a distance of one meter, would exert forces 
on each other of nine billion newtons. This force is roughly the 
same as a weight of one million tons! We never observe such large 
forces, because we could not actually collect that much net charge 
in one place, or exert enough force to bring two such charges so 
close together. The mutual repulsion of like charges is so strong 
that it is difficult to keep a charge of more than a thousandth of a 
coulomb on an object of ordinary size. If you rub a pocket comb on 
your sleeve, enough, say to produce a spark as you touch a doorknob, 
the net charge on the comb will be far less than one millionth of a 
coulomb. Lightning discharges usually take place when a cloud 
has accumulated a net charge of a few hundred coulombs 
distributed over its very large volume. 

Electrostatic induction. We have noted, and you have probably 
observed, that an electrically charged object can often attract 
small pieces of paper even though the paper has no net charge 
itself. (By itself it exerts no force on other pieces of paper.) At first 
sight it might appear that this attraction is not covered by Coulomb's 
law, since the force ought to be zero if either g^ or q^ is zero. 
However, we can explain the attraction if we recall that uncharged 
objects contain equal amounts of positive and negative electric 
charges. When an electrified body is brought near a neutral object, 
its effect can be to rearrange the positions of some of the charges 
in the neutral object. For example, if a negatively charged comb is 
held near a piece of paper, some of the positive charges in the paper 
will shift toward the side of the paper nearest the comb, and a 
corresponding amount of negative charge will shift toward the 
other side. The paper still has no net electric charge, but some of 
the positive charges are then slightly closer to the comb than the 
corresponding negative charges are, so the attraction to the comb 
is greater than the repulsion. (Remember that the force gets weaker 
with the square of the distance, according to Coulomb's law; it 
would be down to one fourth if the distance were twice as large.) 
Hence there will be a net attraction of the charged body for the 
neutral object. This explains the old observation of the effect 
rubbed amber had on chaff and the like. 

A charged body induces a shift of charge on the neutral body. 
Thus the rearrangement of electric charges inside or on the surface 




A stroke of lightning is, on the average, 
about 40,000 amperes, and transfers 
about 1 coulomb of charge between 
the cloud and the ground. 



SG 14.3 



<r' 




-Cv^2U 




42 Electric and Magnetic Fields 

of a neutral body due to the influence of a nearby object is called 
electrostatic induction. In Chapter 16 we will see how the theory 
of electrostatic induction played an important role in the develop- 
SG 14.4, 14.5 ment of the theory of light. 

Q3 In the following sentences, circle what is invented language 
to deal with observation. 

(a) Like charges repel each other. A body that has a net 
positive charge repels any body that has a net positive charge. That 
is, two glass rods that have both been rubbed will tend to repel each 
other. A body that has a net negative charge repels any other body 
that has a net negative charge. 

(b) Unlike charges attract each other. A body that has a net 
positive charge attracts any body that has a net negative charge 
and vice versa. 

Q4 What experimental fact led Priestley to propose that 
electrical force and gravitational forces change with distance in a 
similar way? 

Q5 What two facts about the force between electric charges 
did Coulomb demonstrate? 

Q6 If the distance between two charged objects is doubled, 
how is the electrical force between them affected? 

Q7 Are the coulomb and ampere both units of charge? 

14.4 Forces and fields 

Gilbert described the action of the lodestone by saying it had 
a "sphere of influence" surrounding it. By this he meant that any 
other magnetic body coming inside this sphere will be attracted, 
and the strength of the attractive force will be greater at places 
closer to the lodestone. In modem language, we would say that the 
lodestone is surrounded by a magnetic field. 

Because the word "field" is used in many ways, we shall discuss 
some familiar fields, and then proceed gradually to develop the idea 
of physical fields as used in science. This is a useful exercise 
to remind us that most terms in physics are really adaptations — 
with important changes — of commonly used words. Velocity, 
acceleration, force, energy, and work are examples you have 
already encountered in this course. 

One ordinary use of the concept of field is illustrated by the 
"playing field" in various sports. The football field, for example, is 
a place where teams compete according to rules which confine the 
significant action to the area of the field. The field in this example 
is a region of interaction. 

In international politics, we speak of spheres or fields of 
influences. A field of political influence is also a region of inter- 
action; unlike a playing field, it has no sharp boundary line. A 
country usually has greater influence on some countries and less 
influence on others. So in the political sense, "field" implies also 
an amount of influence, which can be stronger in some places and 



Section 14.4 43 

weaker in others. Furthermore, the field has a source -the country 
that exerts the influence. 

We shall see there are similarities here to the concept of field 
as used in physics, but there is an important diff'erence: to define 
a field in the physical sense, it must be possible to assign a 
numerical value of field strength to every point in the field. This 
part of the field idea will become clearer if we discuss now some 
situations which are more directly related to the study of physics. 
First we will talk about them in everyday language; then we will 
introduce the terminology of physics. 

The Situation Description of your experience 

(a) You are walking along the "The brightness of light is 
sidewalk toward a street lamp at increasing." 

night. 

(b) You stand on the sidewalk "The sound gets louder and 
as an automobile moves down then softer." 

the street with its horn blaring. 

(c) On a hot summer day, you "The sidewalk is cooler here 
walk barefoot out of the sun- than in the sunshine." 

shine and into the shade on the 
sidewalk. 

We can describe these experiences in terms of fields: 

(a) The street lamp is sunounded by a field of illumination. 
The closer you move to the lamp, the stronger the field of illumina- 
tion at the point where you are, as seen by your eye or by a light- 
meter you might be carrying. For every place near the street lamp, 
we could assign a number that represents the strength of 
illumination at that place. 

(b) The automobile horn is surrounded by a sound field. In this 
case you are standing still in your frame of reference (the sidewalk), 
and a pattern of field values goes past you with the same speed as 
the car. We can think of the sound field as steady but moving with 
the horn. At any instant we could assign a number to each point 

in the field to represent the intensity of sound. At first the sound 
is faintly heard as the weakest part of the field reaches you. Then 
the more intense parts of the field go by, and the sound seems 
louder. Finally, the loudness diminishes as the sound field and its 
source (the horn) move away. 

(c) In this case you are walking in a temperature field which 
is intense where the sidewalk is in the sunshine and weaker where 
it is in the shade. Again, we could assign a number to each point 
in the field to represent the temperature at that point. 

Notice that the first two of these fields are each produced by a 
single source. In (a) the source is a stationary street lamp, in (b) it 
is a moving horn. In both cases the field strength gradually 
increases as your distance from the source decreases. But in the 
third case (c) the field is produced by a complicated combination of 
influences: the sun, the clouds in the sky, the shadow cast by nearby 
buildings, and other factors. Yet giving the description of the field 



Pressure and velocity fields 



These maps, adapted from those of the U.S. Weather Bureau, 
depict two fields, air pressure at the earth's surface and high-altitude 
wind velocity, for two successive days. Locations at which the pressure 
is the same are connected by lines. The set of such pressure "contours" 
represents the overall field pattern. The wind velocity at a location is 
indicated by a line (showing direction) and feather lines — one for every 
10 mph. (The wind velocity over the tip of Florida, for example, is a 
little to the east of due north and is approximately 30 mph.) 



Air pressure at the earth's surface 



High altitude wind velocity 




' A ^ 




Iw 



V ^ V V ^ y • 



^ ^- y \ 



r 






J 





/» V 






J J 


• y 


■■■■ 






\'v:ii-iif0h 




i 




•SMiKs 


^ - m^lK. 1 




oii^i'faKl;: ». 




.j^^Hhsk ^ 




«fc-;-:::! 




SBHr " 




^ «. 


K 


v?^^^- 




^ 




jUgpr 




«' v_ ^ 


V 


^ -S^^ 




"" .»' ^ 


V *- 






«. 


V ^ " 






». 


^. 




•- ^ 


V V 


V ^ •" 




•- 


V 


V »- *" ■^ 




•■ v^ 








\^' 


r r 









Section 14.4 



45 



itself is just as simple as for a field produced by a single source: 
one numerical value is associated with each point in the field. 

So far. all examples were simple scalar fields — no direction was 
involved in the value of the field at each point. On the opposite 
page are maps of two fields for the layer of air over the surface of 
North America for two consecutive days. There is a very important 
difference between the field mapped at the left and that mapped 
at the right; the air pressure field (on the left) is a scalar field, while 
the wind velocity field (on the right) is a vector field. For each 
point in the pressure field, there is a single number, a scalar 
quantity which gives the value of the field at that point. But for 
each point in the wind velocity field the value of the field is given 
by both a numerical magnitude and a direction, that is, by a vector. 

These field maps are particularly useful because they can be 
used more or less successfully to predict what the conditions of the 
field might be on the next day. Also, by superimposing the maps 
for pressure and velocity on each other, we could discover how the 
fields are related to each other. 



Wind tpead t21 
to 25 milet pet 

hour I 

Direction of wind. 
iFrom the north- 
wests 

Temperature in 
degree* Fahrenheit 

Total amount of 
clouds iSky com- 
pletely covered I 

Vmbihty (7, 
miles ) 

Present weather 
^Continuous slight 
snow in flakes ) 

Dewpoint in de- 
grees Fahrenheit 

Qoud type iLow 
Iractostratus and/or 
Iractocumulus ) 

Height of cloud 
base [300 to 599 
feet I 



SPECIMEN 
STATION MODEL 




Qoud type iMid 
die altocumulus I 

Barometric pres- 
sure a\ sea level Ini- 
tial 9 or 10 omitted 
{1024 7 millibars i 

Amount of baro- 
metric change in 
past 3 hours ( /n 
tenths of millibars I 

Barometric tend 
ency in past 3 hours 
iRising I 

Sign showing 
whether pressure >s 
higher or lower than 
3 hours ago 

Time preopitatioQ 
began or ended ( Be 
gan 3 to4 hours ago > 

Weather m past 6 
hours (/Join I 

Amount of precipi 
tation in last 6 hours 



The term "field" actually can be used by physicists in three 
different senses: (1) the value of the field at a point in space. (2) the 
collection of all values, and (3) the region of space in which the 
field has values. In reading the rest of this chapter, it will not be 
difficult to decide which meaning is appropriate each time the term 
is used. 

The gravitational force field. Before returning to electricity and 
magnetism, and to illustrate further the idea of a field, we take 
as an example the gravitational force field of the earth. Recall that 
the force Fgrav exerted by the earth on some object above the surface 
of the earth, for example upon a stone or other small object used 
as a test object or "probe," acts in a direction toward the center of 



Key for a U.S. Weather Bureau Map. 



46 



Electric and Magnetic Fields 



\. i 




m 



ۥ 



& 



s\ 



Q 



iW 



SG 14.6 



the earth. The field of force of gravitational attraction set up by the 
earth is a vector field, and could be represented by arrows pointing 
toward the center of the earth. In the illustration, a few such 
arrows are shown, some near, some far from the earth. 

The strength or magnitude of the gravitational force field of the 
earth's attraction on another body at any chosen point depends on 
the distance of the point from the center of the earth, since, 
according to Newton's theory, the magnitude of the gravitational 
attraction is inversely proportional to the square of the distance R: 



= G X 



Mm 
R- 



where M is the mass of the earth, m is the mass of the test body, 
R is the distance between the centers of earth and the other body, 
and G is the universal gravitational constant. 

Fgrav depends on the mass of the test body. It would be con- 
venient to define a field that depends only on the properties of the 
source and not also on the mass of the particular test body on which 
the force acts. If this were possible, we could think of the field as 
existing in space and having a definite magnitude and direction at 
every point, regardless of what the mass of the test body might be, 
or even regardless of whether there is any test body present at all. 
As it happens, such a field is easy to define. By slightly rean-anging 
the equation for Newton's law of gravitation, we can write: 

CM 






We then define the gravitational field strength g around a spherical 
body of mass M to have a magnitude GMIR- and a direction the 
same as the direction of F„rav. so that: 



f = 

* Mrav 



mg 



Thus g at a point in space is determined by the source mass M and 
the distance R from the source, but does not depend on the mass of 
any test object. 

However, the gravitational force at a point in space is usually 
determined by more than one source. For example, the moon is 
acted on by the sun as well as by the earth, and to a smaller extent 
by the other planets. In order to be able to define the field due to 
any configuration of massive bodies, we can take Fgrav to be the 
net gravitational force due to all sources with an influence in that 
region of space. We then define g in such a way that we can still 
write the simple relationship P^^y = mg. That is, we define g by 
the equation: 



9 = 



gray 

m 



Thus the gravitational field strength at a point in space is the ratio 
of the net gravitational force Fgrav which would act on a test body 
at that point to the mass m of the test body. 



Section 14.4 



47 



Electric fields. The strength of any force field can be defined in 
a similar way. According to Coulomb's law, the electric force one 
relatively small charged body exerts on another depends on the 
product of the charges of the two bodies. For a charge q placed at 
any point in the electric field set up by a charge Q, Coulomb's law 
describing the force F^i experienced by q can be written as: 



F =k^ 



F. = q-^ 



As in the case of the gravitational field we discussed earlier, the 
expression for force has here been broken up into two parts. One 
part, kQIR- which depends only on the charge Q of the source and 
distance R from it is given the name "the electric field strength due 
to Q." The second part, q, is a property of the body being acted on. 
Thus we define the electric field strength ^, due to charge Q, to 
have magnitude kQIR^ and the same direction of F^i. The electric 
force is then the product of the test charge and the electric field 
strength: 



n, = q^ 



and 






We consider this equation to define E for an electric force field. 
Thus the electric field strength E at a point in space is the ratio of 
the net electric force F^i which would act on a test charge placed 
at that point to the magnitude q of the test charge. This definition 
can be used whether the electric field being considered is due to a 
single point charge or due to a complicated distribution of charges. 

So far we have passed over a complication that we did not 
encounter in dealing with gravitation. There are two kinds of 
electric charge, positive (+) and negative (— ), and the forces they 
experience when placed in the same electric field are opposite in 
direction. Long ago the arbitrary choice was made of defining the 
direction of the vector £ to be the same as the direction of the force 
exerted by the field on a positive test charge. If we are given the 
direction and magnitude of the field vector E at a point, then by 
definition the force vector Fe, acting on a charge q is F,.i = qE. A 
positive charge, say +0.00001 coulombs, placed at this point will 
experience a force F^i in the same direction as ^ at that point. A 
negative charge, say —0.00001 coulombs, will experience a force of 
the same magnitude as before but in the opposite direction. 
Changing the sign of q from + to — automatically changes the 
direction of Fei to the opposite direction. 

Q8 What is the difference between a scalar field and a vector 
field? Give examples of each. 

Q9 Describe how one can find, by experiment, the magnitude 
and the directions of: 

(a) the gravitational field at a certain point in space 

(b) the electric field at a certain point in space. 

Q10 Why would the field strengths g and E for the test bodies 
be unchanged if m and q were doubled? 



O- 



4 



a 



The reason is that the same kind of 
superposition principle holds which 
we have already seen so many 
times: the fields set up by separate 
sources superpose and add 
vectorially. 

SG 14.7 
SG 14.8 



SG 14.9 



Visualizing electric fields 




Only rarely will we be interested in the 
electric field of a single charged sphere. If we 
want to be able to calculate the field values 
for a complicated array of charges, without 
actually taking some small test charge and 
moving it around in the field to measure the 
force, we need a rule for adding the fields set 
up by separate sources. A wide variety of 
experiments indicates that, at any point in an 
electric field, the field strength produced by 
several sources is just the vector sum of the 
field strengths produced by each source alone. 

A simple example is that of finding the net 
electric field strength produced by a pair of 



spheres with equal charges of opposite sign. 
The first frame above indicates the field 
strength at a point P which would result from 
the presence of the (+) charge alone. The 
second frame shows the field strength at the 
same point which would result from the 
presence of the (-) charge alone. (The point 
P happens to be twice as far from the center 
of the positive charge, so the field strength 
is only j as great in the second frame.) When 
both (+) and (— ) charges are present, the net 
electric field strength at the point P is the 
vector sum of the individual electric field 
strengths, as indicated in the third frame. 




The photograph above shows bits of fine thread 
suspended in oil. At center is a charged object. 
Its electric field induces opposite charges on 
the two ends of each bit of thread which then 
tend to line up end-to-end along the direction 
of the field. 

Top right: equal like charges. 
Bottom right: equal opposite charges. 





The "map" of a three-dimensional electric 
field is not easy to draw. A vector value can 
be assigned to the electric field strength E'at 
every point in space, but obviously we cannot 
illustrate that- such a map would be totally 
black with arrows. A convention which has 
been used for many years in physics is to draw 
a small number of all the infinitely many 
possible lines that indicate the direction of the 
field. For example, the field around a charged 
sphere could be represented by a drawing like 
these above. Notice that the lines, which have 
been drawn symmetrically around the sphere, 
are more closely spaced where the field is 
stronger. The lines can be drawn in three 
dimensions so that the density of lines in a 
given region represents the strength of the 
field in that region. These lines, therefore, 
represent both the local direction and local 
strength of the field, and are called "lines of 



force." Around a single charged sphere the 
lines of force are straight and directed 
radially away from or toward the center. When 
charges are distributed in a more complicated 
way, the lines of force in the region around 
them may be curved. The direction of the field 
strength E'at a point is the tangent to the 
curved line of force at that point. Above, for 
example, we have drawn the lines of force 
that represent the electric field between a 
charged fingertip and the oppositely charged 
surface of a doorknob. The electric field vector 
E'at point P would be directed along the 
tangent to the curved line of force at P, and 
represented by the arrow at P. Note the 
difference: each line of force only shows 
direction, and terminates at a charged object 
or goes off to infinity. But the electric field 
vector E* at each point P is represented by an 
arrow of length drawn to scale to indicate 
magnitude E. 



# 



ft. 



i// 




m 



Oppositely charged plates. (Notice the uniformity of the 
field between the plates as compared with thenonuniformity 
at the ends of the plates.) 



Oppositely charged cylinder and plate. (Notice the 
absence of field inside the cylinder, as indicated by 
lack of alignment of the fibers.) 



so 



Electric and Magnetic Fields 



SG 14.10 Q11 A negatively charged test body is placed in an electric 

field where the vector ^ is pointing downward. What is the direction 
of the force on the test body? 



Milikan used fine droplets of oil 
from an atomizer which become 
charged as they are formed in a 
spray. The oil was convenient 
because of the low rate of evap- 
oration of the droplet. 






1^ 



I r^ 



= mi 



When mg and q? are balanced, fric- 
tional forces remain until the body 
stops moving. 



SG 14.11 



14.5 The smallest charge 

In Sec. 14.3 we mentioned the fact that an electrified comb can 
pick up a small piece of paper, so that in this case the electric force 
on the paper must exceed the gravitational force exerted on the 
paper by the earth. This observation indicates that electric forces in 
general are strong compared to gravitational forces. Another 
illustration of the same point is the fact that we can balance the 
gravitational force on an object, only big enough to be seen in a 
microscope (but still containing several billion atoms) with the 
electrical force on the same object when the object has a net 
electric charge of only a single electron. (The electron is one of the 
basic components of the atom. Other properties of atoms and 
electrons will be discussed in Unit 5.) This fact is the basis of a 
method of measuring the electron's charge in an experiment first 
done by the American physicist Robert A. Millikan in 1909. 
Although a description of Millikan's experiment will be postponed 
until Sec. 18.3, its basic principle will be discussed here because it 
provides such a vivid connection between the ideas of force, field, 
and charge. 

Suppose a small body of mass m — a droplet of oil or a small 
plastic sphere — carries a net negative electric charge of magnitude 
q. If we place the negatively charged body in an electric field E 
directed downwards, a force Fei of magnitude qE will be exerted on 
the body in the upward direction. Of course there will also be a 
downward gravitational force Fgrav = ^ng on the object. The body 
will accelerate upward or downward, depending on whether the 
electric force or the gravitational force is greater. By adjusting the 
magnitude of the electric field strength F. that is by changing the 
source that sets up E — we can balance the two forces. 

What happens when the two forces are balanced? Remember 
that if a zero net force acts on a body it will have no acceleration — 
though it can still be moving with some constant velocity. However, 
in this case air resistance is also acting as long as the drop moves 
at all. and will soon bring the drop to rest. (When the oil drop is 
stationary, no frictional forces of air resistance act on it). The drop 
will then be in equilibrium and will be seen to be suspended in 
mid-air. When this happens, we record the magnitude of the electric 
field strength J^ which we had to apply to produce this condition. 

If the electric force balances the gravitational force, the 
following must hold: 

qE = mg 

We can calculate the charge q from this equation if we know 
the quantities £, m and g. since 

mg 



Section 14,6 



51 



This allows us to find, in the laboratory, what values of charge q 
a small test object such as an oil drop can carry. If you do this, you 
will find the remarkable fact that all possible charges in nature 
are made up of whole multiples of some smallest charge which 
we call the magnitude of the charge on an electron. By repeating 
the experiment many times with a variety of small charges, the 
value of the smallest charge can be found, which is the charge on 
one electron (g^). This is in effect what Millikan did. He obtained 
the value of q^. = 1.6024 x 10""* coulomb for the electron charge. 
(For most purposes we can use the value 1.6 x 10"'" coulomb.) This 
value agrees with the results of many other experiments done 
since then. No experiment has yet revealed the existence of a 
smaller unit of charge. (Some physicists have speculated, however 
that there might be -^Qg associated with a yet-to-be found subatomic 
particle that has been given the name "quark.") 

Q12 How can the small oil droplets or plastic spheres used in 
the Millikan experiment experience an electric force upward if 
the electric field is directed downward? 

Q13 What do the results of the Millikan experiment indicate 
about the nature of electric charge? 



The magnitude of the charge on the 
electron is symbolized by q. and its 
sign is negative. Any charge q is 
therefore given by q = nq,. where n 
Is the whole number of individual 
charges, each of magnitude q... 



SG 14.12-14.14 



14.6 Early research on electric charges 

For many centuries the only way to charge objects electrically 
was to rub them. In 1663, Otto von Guericke made and described 
a machine that would aid in producing large amounts of charge 
by rubbing: 

. . . take a sphere of glass which is called a phial, as large 
as a child's head; fill it with sulphur that has been 
pounded in a mortar and melt it sufficiently over a fire. 
When it is cooled again break the sphere and take out the 
globe and keep it in a dry place. If you think it best, bore 
a hole through it so that it can be turned around an iron 
rod or axle .... 



When he rested his hand on the surface of the sulphur globe 
while rotating it rapidly, the globe acquired enough charge to 
attract small objects. 

By 1750 electrical machines were far more powerful and 
vigorous research on the nature of electricity was going on in many 
places. Large glass spheres or cylinders were whirled on axles 
which were in turn supported by heavy wooden frames. A stuffed 
leather pad was sometimes substituted for the human hands. The 
charge on the globe was often transferred to a large metal object 
(such as a gun barrel) suspended nearby. 

These machines were powerful enough to deliver strong 
electrical shocks and to produce frightening sparks. In 1746 Pieter 
van Musschenbroek, a physics professor at Leyden, reported on 



52 



Electric and Magnetic Fields 




Franklin's drawing of a Leyden jar, 
standing on an insulating block of 
wax. The rod in the stopper was con- 
nected to a conducting liquid in the 
bottle. A charge given to the ball 
would hold through the non-conduct- 
ing glass wall an equal amount of the 
opposite charge on the metal foil 
wrapped around the outside. It can 
hold a large charge because positive 
charges hold negative charges on the 
other side of a nonconducting wall. 




Capacitors, familiar to anyone who 
has looked inside a radio, are de- 
scendents of the Leyden jar. They 
have many different functions in 
modern electronics. 



an accidental and very nearly fatal discovery in a letter which 
begins, "I wish to communicate to you a new, but terrible, 
experiment that I would advise you never to attempt yourself." 
Musschenbroek was apparently trying to conduct the electrical 
genie into a bottle, for he had a brass wire leading from a charged 
gun barrel to a jar filled with water (see illustration on p. 51). A 
student was holding the jar in one hand and Musschenbroek was 
cranking the machine. When the student touched the brass wire with 
his free hand he received a tremendous shock. They repeated the 
experiment, this time with the student at the crank .and Musschen- 
broek holding the jar. The jolt was even greater than before (the 
student must have been giving his all at the crank). Musschenbroek 
wrote later that he thought ". . . it was all up with me . . . ." and 
that he would not repeat the experience even if offered the whole 
kingdom of France. Word of the experiment spread rapidly, and the 
jar came to be called a Leyden jar. Such devices, because of their 
capacity for storing electric charge, are now called capacitators. 

The Leyden jar came to Benjamin Franklin's attention. He 
performed a series of experiments with it, and published his 
analysis of its behavior in 1747. In these experiments Franklin 
first showed that the effects of different kinds of charge (which we 
have called positive and negative) can cancel each other. Because 
of this cancellation he concluded that positive and negative charges 
were not substantially different. Franklin thought that only one 
kind of electricity need be imagined to explain all phenomena. He 
considered a body to be charged positively when it had an excess of 
"electric fire," and to be charged negatively when it had a shortage 
of it. However, this view is no longer held — both positive and 
negative electric charges do exist in their own right. But Franklin's 
theory was sufficient to account for most facts of electrostatics 
known in the eighteenth century. 

Franklin's theory also yielded the powerful and correct idea 
that electric charge is neither created nor destroyed. Charges 
occurring on objects are due to the rearrangement of electric 
charges — an act of redistribution rather than creation. Similarly, 
positive and negative charges can cancel or neutralize each other's 
effect without being destroyed. This is the modern principle of 
conservation of charge, which is taken to be as basic a law of 
nature as are the conservation principles of momentum and of 
energy. The Law of Conservation of Electric Charge can be stated, 
the net amount of electric charge in a closed system remains 
constant, regardless of what reactions occur in the system. Net 
amount of charge is defined as the difference in amounts of + and 
— charge. (For example, a net charge of + 1 coulomb would describe 
1 coulomb of positive charge all by itself, or a composite of 11 
coulombs of positive charge and 10 coulombs of negative charge.) 
If the + and — are taken to be actual numerical signs, instead of 
only convenient labels for two different kinds of charge, then the 
net charge can be called the total charge; adding charges with + 
and — signs will in effect give the difference between the amounts 




of positive and negative charge. The principle of conservation of Electrostatic equipment of the 1700's. 

electric charge is widely useful — from designing circuits (see the 
Reader 4 article, "Ohm's Law") to analyzing subatomic reaction 
(see the Project Physics supplementary unit Elementary Particles). 

An interesting imphcation of the electric charge conservation 
law is that it allows the possibility that charges can appear or 
disappear suddenly in a closed system- as long as there are equal 
amounts of + and - charge. (An example of just such a spontaneous 
appearance of charges is a central part of the experiment in the 
Project Physics film People and Particles.) 



Q14 What experimental fact led Franklin to propose that there 
is only one kind of "electric fire"? 



14.7 Electric currents 

Touching a charged object to one end of a chain or gun barrel 
will cause the entire chain or barrel to become charged. The obvious 
explanation is to imagine that the charges move through the object. 
Electric charges move easily through some materials -called 
conductors. Metal conductors were most commonly used by the SG 14.15 

early experimenters, but salt solutions and very hot gases also 
conduct charge easily. Other materials, such as glass and dry fibers, 
conducted charge hardly at all and are called non-conductors or 
insulators. Dry air is a fairly good insulator. (But damp air is not — 
which is why you may have difficulty in keeping charges on objects 
if you do electrostatic experiments on a humid day.) But if the 
charge is great enough, the air around it will become conducting 
all of a sudden, letting a large amount of charge shift through it. 
The heat and light caused by the sudden rush of charge produces a 
"spark." Sparks were the first obvious evidence of moving charges. 



54 



Electric and Magnetic Fields 




Count Alessandro Volta (1745-1827) 
was given Ills title by Napoleon In 
honor of his electrical experiments. 
He was Professor of Physics at the 
University of Pavia, Italy. Volta showed 
that the electric effects previously ob- 
served by Luigi Galvani, in experiments 
with frog legs, were due to the metals 
and not to any special kind of "ani- 
mal electricity." See the article "A 
Mirror for the Brain" in Reader 4 for 
an account of this controversy. 




Voltaic 'cell' 



Voltaic "pile' 
or battery 



Until late in the eighteenth century, an appreciable movement of 
flow of charge or an electric current, could be produced only by 
discharging a Leyden jar. Such currents last only for the brief 
time it takes for the jar to discharge. 

In 1800, Alessandro Volta discovered a much better way of 
producing electric currents. Volta demonstrated that if different 
metals, each held with an insulating handle, are put into contact 
and then separated, one will have a positive charge and the other 
a negative charge. Volta reasoned that a much larger charge could 
be produced by stacking up several pieces of metal in alternate 
layers. This line of thought led him to undertake a series of 
experiments which produced an amazing finding, reported in a 
letter to the Royal Society in England in March of 1800: 

Yes! the apparatus of which I speak, and which will 
doubtless astonish you, is only an assemblage of a 
number of good conductors of diff"erent sorts arranged in 
a certain way. 30, 40. 60 pieces or more of copper, or 
better of silver, each in contact with a piece of tin, or 
what is much better, of zinc, and an equal number of 
layers of water or some other liquid which is a better 
conductor than pure water, such as salt water or lye and 
so forth, or pieces of cardboard or of leather, etc. well 
soaked with these liquids. . . . 

1 place horizontally on a table or base one of the 
metallic plates, for example, one of the silver ones, and 
on this first plate I place a second plate of zinc; on this 
second plate 1 lay one of the moistened discs; then 
another plate of silver, followed immediately by another 
of zinc, on which I place again a moistened disc. 1 thus 
continue in the same way coupling a plate of silver with 
one of zinc, always in the same sense, that is to say, 
always silver below and zinc above or vice versa, 
according as 1 began, and inserting between these couples 
a moistened disc; 1 continue, 1 say, to form from several of 
these steps a column as high as can hold itself up 
without falling. 

Volta showed that one end, or "terminal," of the pile was 
charged positive, and the other charged negative. He found that 
when wires are attached to the first and last disk of his apparatus 
(which he called a "battery"); it produced electricity with effects 
exactly the same as the electricity produced by rubbing amber, by 
friction in electrostatic machines, or by discharging a Leyden jar. 

But most important of all, Volta's battery provided a means of 
producing a more or less steady electric current for a long period 
of time. Unlike the Leyden jar, it did not have to be charged from 
the outside after each use. Thus the properties of electric currents 
as well as static electric charges could be studied in the laboratory 
in a controlled manner. 

Q15 In what ways was Volta's battery superior to a Leyden jar? 



Section 14.8 



55 



14.8 Electric potential difference 

The sparking and heating produced when the terminals of an 
electric battery are connected show that energy from the battery 
has been transformed into light, sound, and heat energy. The 
battery converts chemical energy to electrical energy which, in 
turn, is changed to other forms of energy (such as heat) in the 
conducting path between the terminals. In order to understand 
electric currents and the way electric currents can be used to 
transport energy, we shall need a new concept that goes by the 
common name "voltage." 

First recall something we learned in mechanics (Unit 3): Change 
in potential energy is equal to the work required to move an object 
frictionlessly from one position to another (Sec. 10.2). For example, 
the gravitational potential energy is greater when a book is on a 
shelf than it is when the book is on the floor; the increase in 
potential energy is equal to the work done raising the book from 
floor to shelf. This difference in potential energy depends on three 
factors: the mass m of the book, the magnitude of the gravitational 
strength field g, and the diff'erence in height d between the floor 
and the shelf. 

In a similar way, the electric potential energy is changed when 
work is done on an electric test charge in moving it from one point 
to another in an electric field, and again, this change of potential 
energy A(P£) can be directly measured by the work that was done. 
The magnitude of this change in potential energy will of course 
depend on the magnitude of the test charge q. So if we divide 
A(PE) by q, we get a quantity that does not depend on how large q 
is, but depends only on the intensity of the electric field and the 
location of the beginning and end points. This new quantity is 
called "electric potential diff'erence." Electric potential difference 
is defined as the ratio of the change in electrical potential energy 
A(P£) of a charge q to the magnitude of the charge. In symbols, 



rn 



I i! f 






1 y V '• '■ -' ' 



,, V 




V 



A(PE) 



The units of electric potential difference are those of energy 
divided by charge, or joules per coulomb. The abbreviation for 
joules/coul is volt; hence the electrical potential difference (or 
"voltage") between two points is 1 volt, if 1 joule of work is done 
in moving 1 coulomb of charge from one of the points to the other. 

1 volt = 1 joule/coulomb 

The potential difference between two points in a steady electric 
field depends on the location of the points, but not on the path 
followed by the test charge. The path can be short or long, direct 
or tortuous — the same work is done per unit charge, just as a 
mountaineer does the same work per pound of mass in his pack 
against the gravitational field from bottom to top of his climb, 
whether he climbs up directly or spirals up along the slopes. Thus 



As is true for gravitational potential 
energy, there is no absolute zero 
level of electric potential energy - 
the difference in potential energy 
is the significant quantity. The 
symbol V is used both for "potential 
difference" as in the equation at the 
left, and as an abbreviation for volt, 
the unit of potential difference (as 
in 1 V = 1 J/coul). 



SG 14.15-14.21 



56 



Electric and Magnetic Fields 




A lT-volt cell is one which has a poten- 
tial difference of li-volts between its 
two terminals. (This type of cell is often 
called a "battery, " although techni- 
cally a battery is the name for a group 
of connected cells.) 




Electrically charged particles (elec- 
trons) are accelerated in an electron 
gun as they cross the potential dif- 
ference between a hot wire (filament) 
and can in an evacuated glass tube. 



it is possible to speak of the electrical potential difference between 
two points in a field, just as it is possible to speak of the difference 
in gravitational potential energy between two points (as we did 
in Sec. 10). 

We begin to see the great influences of this definition of potential 
difference in a simple case. Let us calculate the potential difference 
between two points in a uniform electric field, such as the electric 
field used in the Millikan experiment. Consider two points in a 
uniform electric field of magnitude E produced by oppositely 
charged parallel plates. The work that must be done in moving a 
positive charge q from one point to the other directly against the 
lines of electric force is the product of the force q exerted on the 
charge (Fei = qE). and the distance d through which the charge is 
moved. Thus, 

A(P£) = qEd 

Substituting this expression for A(P£) in the definition of electric 
potential difference gives for the simple case of a uniform field. 

^,_ A(P£) 

<? 
_ qEd 

Q 
= Ed 

In practice it is easier to measure electric potential difference V 
(with a volt-meter) than it is to measure electric field strength E. 
The relationship above is most often useful in the alternative form 
E = VId which can be used to find the intensity of a uniform field. 

Electric potential energy, like gravitational potential energy, 
can be converted into kinetic energy. A charged particle placed in 
an electric field, but free of other forces, will accelerate -it will 
move so as to increase its kinetic energy at the expense of the 
electric potential energy. (In other words, the electric force on the 
charge acts in such a way as to push it toward a region of lower 
potential energy.) A charge q, "falling" through a potential 
difference V, increases its kinetic energy by qV if nothing is lost 
by friction (that is, in a vacuum tube). The increase in kinetic 
energy is equal to the decrease of potential energy: the sum of the 
two at any moment remains constant. This is just one particular 
case of the general principle of energy conservation, when only 
electric forces are acting. 

The conversion of electric potential energy to kinetic energy 
finds application in the electron accelerators (of which a common 
example is a television picture tube). An electron accelerator usually 
begins with an "electron gun" which consists of two basic parts: 
a wire and a metal can in an evacuated glass tube. The wire is 
heated red-hot to cause electrons to escape from its surface. The 
nearby can is charged positively, producing an electric field 
between the hot wire and the can. The electric field accelerates the 
electrons through the vacuum toward the can. Many electrons will 



Section 14.8 



57 



stick to the can, but some go shooting through a hole in one end of 
it. The stream of electrons emerging from the hole can be further 
accelerated or focused by additional cans. (You can make such an 
electron gun for yourself in the laboratory experiment Electron 
Beam Tube.) Such a beam of charged particles has a wide range of 
uses both in technology and in research. For example, it can be 
used to make a fluorescent screen glow, as in a television picture 
tube or an electron microscope. Or it can be used to knock atoms 
apart, producing interesting particles (to study) and x-rays (for 
medical purposes or further research). When moving through a 
potential difference of one volt, an electron with a charge of 1.6 x 
10"'" coulomb increases its kinetic energy by 1.6 x 10"'" joules. 
This amount of energy is called an "electron volt," abbreviated eV. 
Multiples are 1 KeV (= 1000 eV), 1 MeV (= 10« eV) and 1 Bev 
(= 10" eV). Energies of particles in accelerators are commonly 
expressed in such multiples (see Chapter 19). In a TV tube, the 
electrons in the beam are accelerated across an electric potential 
difference of about 20,000 volts — so they each have an energy of 
about 20 KeV. The largest accelerator being constructed now is 
designed to give (for research purposes) charged particles with 
kinetic energies of 200 BeV. 

Q16 How is the electric potential difference, or "voltage," 
between two points defined? 

Q17 Does the potential difference between two points depend 
on the path followed in taking a charge from one to the other? Does 
it depend on the magnitude of the charge moved? 

Q18 Is the electron volt a unit of charge, or voltage, or what? 



Particle accelerators come in a wide 
variety of shapes and sizes. They can 
be as common as a 1000-volt tube 
in an oscilloscope or 20,000-volt TV 
"guns" (see photos on p. 70-71 in 
Study Guide), or as spectacular as 
the one shown below (or the Cam- 
bridge Electron Accelerator which 
was the scene for two Project 
Physics films, People and Particles 
and Synchrotron). 



K : kilo- (10') 

M : mega- (10'') 

B : billion (10'') 

(B is often replaced by G : giga-) 



SG 14.22 

Left: the site of Stanford University's 
2-mile electron accelerator, in which 
electrons are given kinetic energies 
as great as 20 BeV. 
Right: a section of the evacuated tube 
through which the electrons travel. 
The electrons are accelerated in steps 
by electric fields in a long line of ac- 
celerating cavities, similar to those in 
the photograph on p. 30. 




58 



Electric and Magnetic Fields 



In metallic conductors, the moving 
charge is the negative electron, with 
the positive "mother" atom fixed. 
But all effects are the same as if 
positive charges were moving in the 
opposite direction. By an old 
convention, this is the direction 
usually chosen to describe the 
direction of current. 













V^,,i 





Close-up of part of the electric cir- 
cuit in the TV set pictured on p. 40. 
These "resistors" have a fairly con- 
stant voltage-to-current ratio. (The 
value of the ratio is indicated by 
colored stripes.) 

SG 14.23 



14.9 Electric potential difference and current 

The acceleration of an electron in a vacuum by an electric field 
is the simplest example of the effect of a potential difference on a 
charged particle. A more familiar example is electric current in a 
metal wire. Chemical changes inside the battery produce an electric 
field which continually drives charges to the terminals, one 
charged negatively, the other positive. The "voltage" of the battery 
tells us how much energy per unit charge is available when the 
electric field between the terminals is allowed to move charges in 
any external path from one terminal of the battery to the other. 

The relation between current and potential difference might 
seem to be more complicated in a wire than a vacuum tube because 
electrons in a metal do not move freely as they would in an 
evacuated tube, but are continually interacting with the atoms 
of the metal. However, there is a simple relation, originally found 
by experiment by George WUhelm Ohm. which is at least 
approximately valid in the case of most metallic conductors: the 
total current I in a conductor is proportional to the potential 
difference V applied between the two ends of the conductor. If we 
use the symbol I for the current and V for the applied potential 
difference, we can write the relationship as 

/ cc V 
or / = constant x V 

This simple proportionality is called Ohm's Law. It is usually 
written in the form 

where R is a constant called the resistance of the conducting path. 
Thus, Ohm's law assumes that the amount of the resistance of a 
given conducting path does not depend on current or voltage. The 
resistance does depend on the material and dimensions of the path, 
such as the length and diameter of the wire. The resistance is not 
strictly a constant for any conducting path — it varies with changes 
in temperature, for example. 

Ohm's law is a good empirical approximation in practical 
technical work, but it does not have the status and generality of 
such laws as the law of universal gravitation or Coulomb's law. 
In this course, we will use it mainly in lab work and in connection 
with the discussion of electric light bulbs and power transmission 
in Chapter 15. 

Q19 How does the current in a metallic conductor change if 
the potential difference between the ends of the conductor is 
doubled? 

Q20 What does it mean to say a resistor has a resistance of 
5 megohms (5 x 10" ohms)? 

Q21 How would you test whether Ohm's law applies to a given 
piece of wire? 



Section 14.10 



59 



14.10 Electric potential difference and power 

If the charge could move freely from one terminal to the other 
in an evacuated tube, the work done on the charge would simply 
increase the kinetic energy of the charge. However, if the charge 
moves through some material such as a wire or resistor, it will 
transfer energy to the material by colliding with atoms; thus at 
least some of the work will go into heat energy. If, for example, 
the battery is forcing charges through the filament wire in a 
flashlight bulb, the electric energy carried by the charges is 
dissipated in heating the filament. (The hot filament radiates 
energy, a small fraction of which is in the form of visible light.) 
Recall now that "voltage" (electric potential difference) is the 
amount of work done per unit of charge transferred per unit time. 
So the product of voltage and current will be the amount of work 
done per unit time: 




V (joules/coulomb) x I (coulombs/sec) = VI (joules/sec) 

But work done per unit time is called power (as defined in Sec. 
10.6 of Unit 3 Text). The unit of power, equal to 1 joule/sec, is 
called a "watt." Using the definition of ampere (1 coulomb/sec) 
and volt (1 joule/coulomb), we can write the power P: 

P (watts) = V (volts) X I (amperes) 

What energy transformation does this work accomplish? As 
the positive charge moves to a lower potential level, it does 
work against material by colliding with its atoms, and the 
electrical energy associated with it is converted into heat energy. 
If V is the voltage between the two ends of some material carrying 
a current I, the power dissipated in the material as heat will be 
given by P = VI. This can be equally well expressed in terms of the 
resistance of the material substituting IR for V: 



Example: A small flashlight bulb 
connected to a 1.5-volt cell will have 
a current of about 0.1 ampere in its 
filament. At what rate is electric 
work being done to heat the 
filament in the bulb? 
P = W 

= 1.5 volts X 0.1 amps 

= 0.15 watts 
(Only a small fraction of this power 
goes into the visible light energy 
radiated from the filament.) 



IR X J 
PR 



SG 14.24-14.27 



Joule was the first to find experimentally that the heat produced 
by a current is proportional to the square of the current. This 
discovery was part of his series of researches on conversion of 
different forms of energy (described in Sec. 10.8). The fact that the 
rate of dissipation of energy is proportional to the square of the 
current has great significance in making practical use of electric 
energy, as we will see in the next chapter. 

Q22 What happens to the electrical energy used to move 
charge through a conducting material? 

Q23 How does the power dissipated as heat in a conductor 
change if the current in the conductor is doubled? 



60 



Electric and Magnetic Fields 



14.11 Currents act on magnets 





A useful rule: if the thumb points in 
the direction of the flow of charge, the 
fingers curl in the direction of the 
lines of the magnetic field 5. The mag- 
nitude of 3 is discussed in Sec. 14.13. 
Use the right hand for positive charge 
flow, left hand for negative charge 
flow. 



Since early in the eighteenth century there were reports that 
lightning had changed the magnetization of compass needles and 
had made magnets of knives and spoons. Some believed that they 
had magnetized steel needles by discharging a Leyden jar through 
them. These reports suggested that electricity and magnetism are 
intimately related in some way. But the casual observations were 
not followed up with deliberate, planned experiments that might 
have had an impact on the development of concepts and theory. 

None of these early reported occurrences surprised adherents 
of the Nature Philosophy current in Europe at the start of the 
nineteenth century. They were convinced that all the observed 
phenomena in nature were different manifestations of a single 
force. Their metaphysical belief in the unity of physical forces 
would, in fact, lead them to expect that electrical and magnetic 
forces were associated or related in some way. 

The first concrete evidence of a connection between electricity 
and magnetism came in 1820. when Oersted performed a 
momentous series of experiments. (See illustrations on next page.) 
Oersted placed a magnetic compass needle directly beneath a long 
horizontal conducting wire. He had placed the wire along the 
earth's magnetic north-south line, so that the magnetic needle 
was naturally aligned parallel to the wire. When the wire was 
connected to the terminals of a battery, the compass needle swung 
toward an east- west orientation — nearly perpendicular to the wire! 
While charge at rest does not affect a magnet, charge in motion 
(a current) does exert an odd kind of force on a magnet. 

Oersted's results were the first instance ever found in which a 
force was observed that did not act along a line connecting the 
sources of the force (as forces do between planets, or between 
electric charges, or between magnetic poles). The force that the 
current-carrying wire exerts on a magnetic pole is not along the 
line from the wire to the pole: the force that must be acting on the 
pole to twist is necessarily acting perpendicular to such a line. 
The magnetic needle is not attracted to or repelled by the wire that 
carries the current: it is twisted sidewise by forces on its poles. 

The way a current affects a compass needle certainly seemed 
peculiar. No wonder it had taken so long before anyone found the 
connection between electricity and magnetism. Closer examination 
revealed more clearly what was happening in all these experiments. 
The long straight current-carrying wire sets up a magnetic field 
that turns a small magnet so that the north-south line on the 
magnet is tangent to a circle whose center is at the wire and whose 
plane lies perpendicular to the wire. Thus, the current produces a 
circular magnetic field, not a central magnetic field as had been 
expected. 

We define the direction of the magnetic field vector B at each 
point to be the same as the direction of the force on the north- 
seeking pole of a compass needle placed at that point. The force 




To make the photograph below, a thick wire was inserted vertically 
through a horizontal sheet of cardboard, and tiny slivers of iron were 
sprinkled on a sheet. A strong current through the wire creates a magnetic 
field which causes the slivers to become magnetized and to line up in 
the direction of the field. Note that the magnetic lines of force encircle 
the wire. 



Hans Christian Oersted (1777-1851), a 
Danish physicist, studied the writings of 
the Nature Philosopher Schelling and 
wrote extensively on philosophical sub- 
jects himself. In an essay published in 
1813, he predicted that a connection be- 
tween electricity and magnetism would 
be found. In 1820 he discovered that a 
magnetic field surrounds an electric 
current when he placed a compass under 
a current-carrying wire. In later years he 
vigorously denied the suggestion of other 
scientists that his discovery of electro- 
magnetism had been accidental. 




Oersted's experiment 



<7> 



«3? 






o> 



<^ 



^ 



<2S 



C5 



o 



<r.> 



<7> 








Left: an array of tiny compasses on a sheet of cardboard placed 
perpendicular to a brass rod. Right: when there is a strong current 
in the rod, the compass needles are deflected from their normal 
north-south line by the magnetic field set up by the current. This 
experiment, too, indicates that the lines of magnetic force due to 
the current are circular around the rod. 



62 



Electric and Magnetic Fields 




Needle-like iron oxide crystals in the 
magnetic field of a bar magnet. The 
bar magnet is under the paper on 
which the iron oxide has been spread. 



'^r ^ S i^'&WMWc 




Iron filings in the magnetic field pro- 
duced by current in a coil of wire. 



SG 14.28 



on the south-seeking pole will be in a direction exactly opposite to 
the field direction. A compass needle will respond to the opposite 
forces on its ends by turning until it points as closely as possible 
in the direction of the field. We can get a clue to the "shape" of the 
magnetic field set up all around a current by sprinkling tiny slivers 
of iron on a sheet of paper through which the current-carry-ing wire 
is passing. The slivers become magnetized and serve as tiny 
compass needles to indicate the direction of the field. Since the 
slivers also tend to link together end-to-end. the pattern of slivers 
indicates magnetic hnes of force around any current-carrying 
conductor or for that matter around a bar magnet. These lines form 
a pictorial representation of the magnetic field. 

An example of such pictorialization is finding the "shape" of 
magnetic field produced by a current in a coil of wire, instead of a 
straight piece of wire. To do this, we bend the wire into a loop so 
that it goes through the paper in two places. The magnetic effects 
of the different parts of the wire on the iron slivers combine to 
produce a field pattern similar to that of a bar magnet. (See pp. 64 
and 65.) 

Q24 Under what conditions can electric charges affect magnets? 

Q25 What was surprising about the force a current exerted on 
a magnet? 

Q26 How do we know that a current produces any magnetic 
field near it? What is the "shape" of the field anywhere near a 
straight conductor? 



'- « 


X--^^-m 




Ml 



Andre-Marie Ampere (1775-1836) was 
born in a village near Lyons, France. 
There was no school in the village and 
Ampere was self-taught. His father 
was executed during the French Revo- 
lution, and Ampere s personal life was 
deeply affected by his father s death. 
Ampere became a professor of mathe- 
matics in Paris and made important 
contributions to physics, mathematics, 
and the philosophy of science. His 
self-portrait is reproduced above. 



14.12 Currents act on currents 

Oersted's discovery* is a typical case of the rare occasion when 
a discovery opens up an exciting new subject of research. In this 
case, no new equipment was needed. At once, scores of people in 
laboratories throughout Europe and America began intensive 
studies on the magnetic effects of electric currents. The work of 
Andre-Marie Ampere (1775-1836) stands out among all the rest. 
Ampere came to be called the "Newton of electricity" by James 
Clerk Maxwell, who some decades later was to construct a 
complete theory of electricity and magnetism. Ampere's work 
is filled with elegant mathematics; without describing his theor\- 
in detail, we can trace some of his ideas and review some of 
his experiments. 

Ampere's thoughts raced forward as soon as he heard Oersted's 
news. He began with a line of thought somewhat as follows: since 
magnets exert forces on each other, and since magnets and 
currents also exert forces on each other, can it be that currents 
exert forces on other currents? Although it is tempting to leap 
forward with a reply, the answer is not necessarily yes. Arguing 
from symmetry is inviting and often turns out to be right, but it is 



Section 14.12 



63 



not logically or physically necessary. Ampere recognized the need 
to let experiment provide the answer. He wrote: 

When M. Oersted discovered the action which a current 
exercises on a magnet, one might certainly have sus- 
pected the existence of a mutual action between two 
circuits carrying currents; but this was not a necessary 
consequence; for a bar of soft iron also acts on a 
magnetised needle, although there is not mutual action 
between two bars of soft iron. 

And so Ampere put his hunch to the test. On September 30, 
1820, within a week after word of Oersted's work reached France, 
Ampere reported to the French Academy of Sciences that he had 
indeed found that two parallel current-carrying wires exert forces 
on each other even though they showed no evidence of electric 
charges. 

Ampere made a thorough study of the forces between currents, 
and how they depend on the distance between the wires and their 
relative orientations as well as on the amount of current. In the 
laboratory you can repeat these experiments and work out the "force 
law" between two currents. We will not need to go into the 
quantitative details here, except to note that the force between 
currents can be used to measure how much current flows. In fact, 
the magnetic force between currents is nowadays the preferred way 
to define the unit of current, which is called the ampere (as 
mentioned in Sec. 14.3). One ampere is defined as the amount of 
current in each of two long straight parallel wires set one meter 
apart, which causes force of exactly 2 x lO " newtons on each 
meter of the wires. 





'i 




^ 



Replica of Amperes current balance. 
The essential part is a fixed horizontal 
wire (foreground), and just behind it, 
hanging from a hinged support, a 
shorter segment of wire. Current is 
produced in both wires, and the force 
between them is measured. 



Q27 What was Ampere's hunch? 



Summary of 
Quantity 



potential 
difference 



electric 
power 



Electric Units 
Symbol Unit 



electric 
field 



magnetic 
field 



The ampere is tfie fourth fundamental unit in the so-called MKSA system 
(meter, kilogram, second, ampere) which is now widely used by physicists. For 
definition, see last paragraph. 

The coulomb is defined as the amount of charge that flows in one second, 
when the current is 1 ampere. 

The volt is defined as the electric potential difference between two points 
such that 1 joule of work is done in moving 1 coulomb of charge between those 
points. 

The wait is defined as the rate of energy flow (or work done per second, or 
"power") which corresponds to 1 joule per second. Thus a current of 1 ampere 
due to a potential difference of 1 volt corresponds to 1 watt of power. The 
kilowatt IS equal to 1000 watts. 

The kilowatt-hour is the amount of energy expended (work done) when one 
kilowatt of power is used for one hour. It is equal to 3,600,000 joules (1000 
joules/sec x 3600 sec). 

The ohm is defined as the resistance of a material which allows a current 
of just 1 ampere to pass through if the potential difference across the material 
IS 1 volt. 

Electric field can be expressed either in terms of the force experienced by 
a unit charge (newtons per coulomb), or in terms of the rate at which the electric 
potential difference increases (volts per meter). 

The magnitude of magnetic field is defined in terms of the force experienced 
per meter of length by a conductor carrying a current of 1 ampere. The units 
are thus newtons per ampere-meter. Another common unit is the gauss, which 
equals 10"* newtons/amp. meter. 



Magnets and fields 

The diagrams at the right represent the magnetic field of a current 
in a loop of wire. In the first diagram, some lines of force due to 
opposite sides of the loops have been drawn separately. One example 
is given of how the two fields add at point P. Some lines of force for 
the total field are drawn in the second diagram. Below at the right is 
a photograph of iron filings in the magnetic field of an actual current 
loop. Below at the left is the field of a series of coils, or helix. 

In many applications, from doorbells to cyclotrons, magnetic 
fields are produced by coils of wire wound around iron cores. When 
a current is switched on, the iron core becomes magnetized and 
increases the strength of the field of the coil alone by a factor of 10- 
or 10^. Such devices are called electromagnets. 



X 



/ 4r' 






\ / 





f<^ 



^Mi^~ 




►■/ 1' ''h V, ^Jv••■^.A• -,^V;-t^^ -.sw--.^-., — r^y .i a/ / '!•;.' t.ii". i 






•^f^hV -/ » V4i . 





This electromagnet was used early in 
this century to deflect a beam of 
charged atoms sent through the tube 
at the top, in the gap between two sets 
of coils. It appears again in Unit 6. 





A modern electromagnet used in re- 
search when strong uniform fields are 
required. 



The first electromagnet, invented by William Sturgeon in Eng- 
land in 1824, could lift a weight of nine pounds. In 1832, Joseph 
Henry constructed an electromagnet at Princeton which could 
hold up a weight of 3,600 pounds. Modern electromagnets 
(see above) which can typically lift 50,000 pounds of iron are 
widely used in Industry, for example, to sort or load scrap metal. 




In the two pictures at the left, iron 
nails line up in a strong magnetic 
field produced by large currents in 
superconducting coils, kept at 4° 
above absolute zero by liquid helium. 



66 Electric and Magnetic Fields 

14.13 Magnetic fields and moving charges 

In the last two sections we discussed the interactions of currents 
with magnets and with each other. The description of these 
phenomena is greatly simplified by the use of the concept of 
magnetic field. 

As we saw in studying Coulomb's law. electrically charged 
bodies exert forces on each other. When the charged bodies are at 
rest, we say that the forces are "electric" forces, or Coulomb forces, 
and we imagine "electric fields" which are responsible for them. 
But when the charged bodies are moving with respect to us (as for 
example when two parallel wires carry currents), new forces in 
addition to the electric forces are present. We call these new forces 
"magnetic" and attribute them to "magnetic fields" set up by the 
moving charges. 

The magnetic interaction of moving charged bodies is not as 
simple as the electric interaction. As we saw in the description of 
Oersted's experiment, the direction of the force exerted by a current 
on a magnet needle is perpendicular both to the direction of the 
cuiTent and to the line between the magnet and current. For the 
moment, however, we will not be concerned about the forces on 
current-carrying conductors. Instead, we will consider the behavior 
of individual, freely moving electric charges in an external magnetic 
field. We believe, after all, that the force on a wire is due to the 
force on the moving electric charges in it. Once we have established 
some simple rules for the behavior of free charged particles, we 
will return to wires again in the next chapter. There you will see 
how the simple rules are sufficient to understand the operation of 
electric generators and electric motors — and how these inventions 
transformed western civilization. But seeking simple rules is not 
the only reason for considering individual charged particles. The 
behavior of individual charged particles in a magnetic field is basic 
to understanding a wide range of phenomena, from television 
picture tubes to cyclotrons and radiation belts around the earth. 

The rules summarized in the remainder of the section are best 
learned in the laboratory. All you need is a magnet and a device to 
'' produce a beam of charged particles — for example, the "electron 

gun" described in Sec. 14.8. (Recommended procedures are described 
in the experiment Electron Beam Tube in the Handbook.) 

,, ,.,. ., , . - The force on a moiling charged body. Suppose we have a fairly 

(a) When q moves with velocity v •' _^a z> ^ tt 

perpendicular to S'we find that uniform magnetic field B (which may be produced either by a bar 

magnet or by a current in a coil), and we study how this external 

field acts on a moving, charged body. We find by experiment that 

the charge experiences a force, and that the force depends on 

three quantities: the charge q on the body, the velocity v of the 

body, and the strength of the external field B* through which the 

body is moving. The force depends not only on the magnitude of 

the velocity, but also on its direction. If the body is moving in a 

(b) there IS a force V as shown. direction perpendicular to the field B, the magnitude of the force 
proportional to q, v. and 6 is proportional to each of these quantities, that is. 



^ 



B 



r- 



Section 14.13 



67 



F °^ qvB 
which we can also write as 

F = kqvB 

where fe is a proportionahty constant that depends on the units 
chosen for F, q, v, and B. If the charge is moving in a direction 
parallel to B*, there is no force! For all other directions of motion, 
the force is between the full value and zero. In fact, the force is 
found to be proportional to the component of the velocity perpen- 
dicular to the field direction, v _. Hence we can write a more general 
expression for the force: 

F ^ qv B 
or F = kqv B 

where k is the same constant as before. The direction of the force 
is always perpendicular to the direction of the field and is also 
perpendicular to the direction of motion of the charged body. 

The force exerted by an external magnetic field on a moving 
charged particle can be used to define the unit of magnetic field B*. 
by taking the proportionahty constant in the last equation equal to 
one. This definition of the unit of b" will be convenient here since 
we will be mainly concerned with how magnetic fields act on 
moving charges (rather than with forces between bar magnets). 
So in the special case when B and iTare at right angles to each 
other, the magnitude of the deflecting force becomes simply 

F = qvB 

The path of a charged body in a magnetic field. The force on a 
moving charged body in a magnetic field is always "off to the side. " 
that is, perpendicular to its direction of motion at ever>' moment. 
Therefore, the magnetic force does not change the speed of the 
charged body, but it does change the direction of the velocity vector. 
If a charged body is moving exactly perpendicular to a uniform 
magnetic field, there will be a constant sideways push and the body 
will move along a circular path, in a plane perpendicular to the 
direction of the magnetic field. If B is strong enough, the particle 
will be trapped m a circular orbit (as in the upper sketch a in 
the margin). 

What happens if the charged body's velocity has some com- 
ponent along the direction of the field but is not exactly parallel 
to it? The body will still be deflected into a curved path, but at the 
same time, the component of its motion along the field will continue 
undisturbed; so the particle will trace out a coiled (helical) path, 
(as in the lower sketch b in the margin). If the body is initially 
moving exactly parallel to the magnetic field, there is no deflecting 
force on it at all, since in this case, v^ is zero. 

Some important examples of the deflection of charged particles 
by magnetic fields to be discussed in Units 5 and 6 will include 
particle accelerators and bubble chambers. Here we will mention 
one important example of the "coiled" motion: the Van Allen 
radiation belts. A stream of charged particles, mainly from the 



(c) If 7is not 1 toe, there is a smaller 
force, proportional to v instead of v. 



A useful rule: if 
your fingers point 
along ^, and your 
thumb along 1/, 
f'will be in the di- 
rection your palm 
would push. For 
positive charges 
use the right hand. 
and for negative 
use the left hand. 





SG 14.31 



68 



Electric and Magnetic Fields 




A simplified sketch of a variety of 
paths taken by charged particles in 
the earth's magnetic field. The Van 
Allen belts are regions of such trapped 
particles. 



The American physicist James A. 
Van Allen directed the design of 
instruments carried by the first 
American satellite, Explorer I. See 
his article "Radiation Belts Around 
the Earth," in Reader 4. 

SG 14.32, 14.33 



sun but also from outer space. conttnuaDy sweeps past the earth. 
Many of these particles are deflected into spiral paths by the 
magnetic field of the earth, and are subsequently "trapped" in 
the earth's field. The extensive zones containing the rapidly 
moving trapped particles are called the Van Allen belts. When 
some of the particles from these zones work their way toward the 
earth's magnetic poles and hit the atmosphere, they excite the 
atoms of the gases to radiate light. This is the cause of the aurora 
(■"northern lights" and "southern lights"). 

In this chapter we have discussed the interaction between 
currents and magnets and between magnetic fields and charged 
particles. At first reading, many students consider this topic to be 
a very abstract part of pure physics. Yet as you should see at once 
in the next chapter, and again in Chapter 16. the study of these 
interactions has had important social and practical consequences 
for the whole civilized world. 

Q28 Which of the following affect the magnitude of the 
deflecting force on a moving charged particle? 

(a) the component of the velocity parallel to the magnetic field 

(b) the component of the velocity perpendicular to the field 

(c) the magnetic field B itself 

(d) the magnitude of the charge 

(e) the sign of the charge 

Q29 Which of the items in the preceding question aff'ect the 
direction of the deflecting force on the charged particle? 

Q30 Why does the deflecting force on a moving charged 
particle not change the speed of the charged particle? Does it ever 
do any work on it? 

Q31 What are differences between deflecting forces on a 
charged object due to gravity, due to an electric field, and due to a 
magnetic field? 



The aurora photographed from Alaska. 
The glow is produced when the upper 
atmosphere is excited by charged par- 
ticles trapped in the earth's magnetic 
field. 




STUDY GUIDE 



14.1 The Project Physics learning materials 
particularly appropriate for Chapter 14 include: 

Experiments 

Electric Force I 

Electric Forces II 

Currents, Magnets, and Forces 

Electron Beam Tube 
Activities 

Detecting Electric Fields 

Voltaic Pile 

An 11(? Battery 

Measuring Magnetic Field Intensity 

More Perpetual Motion Machines 

Additional Activities Using the Electron 
Beam Tube 

Inside a Radio Tube 

An Isolated North Magnetic Pole? 
Reader Articles 

Radiation Belts Around the Earth 

A Mirror for the Brain 

14.2 How much must you alter the distances 
between two charged objects in order to keep 
the force on them constant, if you also 

(a) triple the net charge on each? 

(b) halve the net charge on each? 

(c) double the net charge on one and halve the 
net charge on the other? 

14.3 How far apart in air must two charged 
spheres be placed, each having a net charge of 
1 coulomb, so that the force on them is 1 
newton? 

'''*.4 If electrostatic induction does not involve 
the addition or subtraction of charged particles, 
but instead is just the separation, or redistribution, 
of charged particles, how can you explain the fact 
that attraction results from induction? 

14.5 A carbon-coated (and therefore conducting) 
ping-pong ball hanging by a nylon (nonconducting) 
thread from a ring stand is touched with a finger 
to remove any slight charge it may have had. 
Then a negatively charged rod is brought up close 
to but not touching the ball. While the rod is held 
there the ball is momentarily touched with a 
finger; then the rod is removed. Does the ball now 
have a net charge? How would you test whether 
it has. If you think it has, make a few simple 
sketches to show how it became charged, in- 
dicating clearly what kind of charge it has been 
left with. 

14.6 (a) Calculate the strength of the gravita- 

tional field of the moon at a point on its 
surface. The mass of the moon is 
taken to be 7.3 x 10" kg and its radius 
is 1.74 X 10" m. 

(b) Calculate the gravitational field at a 
point near the surface of a small but 
extremely dense star, LP357-186, whose 
radius is 1.5 x lO*' m and whose density 
is about 10^- kg/m^. 

(c) The gravitational field of any uniform 
spherical shell is zero inside the shell. 



Use this principle together with New- 
ton's gravitational force law and the 
formula for the volume of a sphere 
(fTrr^) to find out how the gravitational 
field at a point P inside a solid 
spherical planet depends on the 
distance r from the center. (Assume 
the planet's density is uniform 
throughout.) 




14.7 We speak of an electric field exerting a 
force on a charged particle placed in the field. 
What has to be true about this situation in view 
of the fact that Newton's third law holds in 
this case too? 

14.8 The three spheres A, B and C are fixed in 
the positions shown. Determine the direction of 
the net electrical force on sphere C, which is 
positively charged, if 



© 



€) 



© 



(a) A and B carry equal positive charges. 

(b) A and B have charges of equal magnitude, 
but the charge on B is negative, and on A 
is positive. 

14.9 An electric field strength exists at the 
earth's surface of about 100 N/coul, directed 
downward. 

(a) What is the net charge on the earth? (As 
Newton had shown for gravitational forces, 
the field of a uniformly charged sphere can 
be calculated by assuming all of the charge 
is concentrated at its center). 

(b) Because the earth is a conductor, most of 
the net charge is on the surface. What, 
roughly, is the average amount of net 
charge per square meter of surface? Does 
this seem large or small, compared to 
familiar static charges like those that can 
be produced on combs? 

14.10 In oscilloscope tubes, a beam of electrons 
is deflected as it is passed between two pairs of 
oppositely charged plates. Each pair of plates, 

as can be seen in the photograph at the top of the 
following page, is shaped something like the 



69 



oiuuT vauiuc 




sketch to the right of the photograph. Sketch in 
roughly what you think the lines of force in the 
electric field between a pair of such oppositely 
charged plates would be like. 

14.11 Is air friction acting on the moving oildrop 
a help or a hindrance in the experiment described 
for measurement of the charge of the electron. 
Explain your answer briefly. 

14.12 The magnitude of the electrons charge 
will be seen later to be 1.6 x 10"'* coulomb. How 
many electrons are required to make 1 coulomb 
of charge? 

14.13 Calculate the ratio of the electrostatic 
force to the gravitational force between two 
electrons a distance of 10''° meters apart. (The 
mass of the electron is approximately 10"^° kg; 
recall that G = 6.7 x lO"" N-m'^/kg^) 

14.14 Because electrical forces are similar in 
some respects to gravitational forces, it is 
reasonable to imagine that charged particles 
such as the electron, may move in stable orbits, 
around other charged particles. Then, just as the 
earth is a "gravitational satellite" of the sun, 
the electron would be an "electric satellite" of 
some positively charged particle that has a mass 
so large compared to the electron that it can be 
assumed to remain stationary at the center of the 
electron's orbit. Suppose the particle has a charge 
equal in magnitude to the charge of the electron, 
and that the electron moves around it in a 
circular orbit. 

(a) The centripetal force acting on the moving 
electron is provided by the electrical 
(Coulomb) force between the electron and 
the positively charged particle. Write an 
equation representing this statement, and 
from this equation derive another equation 
that shows how the kinetic energy of the 
electron is related to its distance from the 
positively charged particle. 

(b) Calculate the kinetic energy of the electron 
if the radius of its orbit were 10"'" meters. 

(c) What would be the speed of the electron if 
it had the kinetic energy you calculated in 
part (b)? (The mass of the electron is 
approximately 10"^ kg.) 

14.15 A hard-rubber or plastic comb rubbed 
against wool can often be shown to be charged. 



Why does a metal comb not readily show a net 
charge produced by rubbing unless it is held by 
an insulating handle? 

14.16 What is the potential difference between 
two points in an electric field if 6 x lO"* joules of 
work were done against the electric forces in 
moving 2 x IQ » coulombs of charge from one 
point to the other? 

14.17 If there is no potential difference between 
any points in a region, what must be true of 

(a) the electric potential energy and 

(b) the electric field in that region? 

14.18 Electric field intensity. E can be measured 
in either of two equivalent units: newtons-per- 
coulomb, and volts-per-meter. Using the definitions 
of volt and joule, show that newton is actually 
the same as volt/meter. Can you give the reason 
for the equivalence in words? 

14.19 By experiment, if the distance between the 
surfaces of two conducting spheres is about 1 cm, 
an electric potential difference of about 30,000 
volts between them is required to produce a spark 
in ordinary air. (The higher the voltage above 
30.000 V. the "fatter" the spark for this gap 
distance.) What is the minimum electric field 
strength (in the gap between the surfaces) 
necessary to cause sparking? 

14.20 The gap between the two electrodes in an 
automobile sparkplug is about 1 mm (39 thou- 
sandths of an inch). If the voltage produced 

between them by the ignition 
coil is about 10.000 volts, what 
is the approximate electric field 
strength in the gap? 




14.21 One can think of an electric battery as 
"pumping" charges onto its terminals up to 
the point where electric potential difference 
between the terminals reaches a certain value, 
where those charges already there repel 
newcomers from inside the battery; usually the 
value is very close to the voltage marked on 
the battery. 

What would happen if we connected two or 
more batteries in a sequence? For example, the 



70 



battery on the right, below, maintains terminal C 
at an electric potential 6 volts higher than 



(-; 




terminal D. This is what the + indicates under 
C — its electric potential is higher than the 
other terminal of the same battery. The battery 
on the left maintains terminal A at a potential 
6 volts higher than terminal B. If we connect B 
to C with a good conductor, so that B and C 
are at the same potential level, what is the 
potential difference between A and D? What 
would the potential difference be between the 
extreme left and right terminals in the follow- 
ing set-ups? 




14.22 (a) What kinetic energy will an electron 

gain in an evacuated tube if it is 
accelerated through a potential differ- 
ence of 100 volts. State your answer 
in electron volts and also in joules. 
(The magnitude of the charge on the 
electron is 1.6 x 10 '" coulomb.) 
(b) What speed will it acquire due to the 
acceleration? (The mass of the 
electron is 10"^" kg.) 

14.23 Suppose three resistors are each connected 
to a battery and to a current meter. The following 
table gives two of three quantities related by 
Ohm's law for three separate cases. Complete 
the table. 

Voltage Current Resistance 

(a) 2 volts 0.5 ohms 

(b) 10 volts 2 amps 

(c) 3 amps 5 ohms 

14.24 The electric field at the earths surface can 
increase to about 10" volts/meter under thunder 
clouds. 

(a) About how large a potential difference 
between ground and cloud does that imply? 

(b) A set of lightning strokes can transfer as 
much as 50 coulombs of charge. Roughly 
how much energy would be released in 
such a discharge? 



14.25 "Physics International's B^ Pulsed 
Radiation Facility is now producing the world's 
most intense electron beam (40,000 amps/4 MeV) 
as a routine operation. With this beam PI can 
precisely deposit upwards of 5,000 joules of energy 
in 30 nanoseconds." (Physics Today, Dec. 1966). 

The "4MeV" means that the charges in the 
beam have an energy that would result from 
being accelerated across a potential difference 
of 4 million volts. A "nanosecond" is a billionth 
of a second. Are these published values con- 
sistent with one another? (Hint: calculate the 
power of the beam in two different ways.) 

14.26 An electron "gun" includes several elec- 
trodes, kept at different voltages, to accelerate 
and focus the electron beam. Nonetheless, the 
energy of electrons in the beam that emerges 
from the gun depends only on the potential 
difference between their source (the hot wire) and 
the final accelerating electrode. In a color-tv 
picture tube, this potential difference is 20 to 

30 kilovolts. A triple gun assembly (one each for 
red, blue, and green) from a color set is shown in 
the photograph below. 




If the beam in a TV tube is accelerated 
through 20,000 volts and constitutes an average 
current on the order of 10"^ amps, roughly what 
is the power being dissipated against the screen 
of the tube? 

14.27 Calculate the power dissipated in each of 
the three circuit elements of question 14.23. 

14.28 A student who wished to show the magnetic 
effect of a current on a pocket compass, slowly 
slid the compass along the tabletop toward a 
wire lying on the table and carrying a constant 
current. He was surprised and puzzled by the 
lack of any noticeable turning effect on the 
compass needle. How would you explain his 
unexpected result? 

14.29 The sketch shows two long, parallel wires, 
lying in a vertical north-south plane (the view 
here is toward the west). A horizontal compass is 
located midway between the two wires. With no 
current in the wires, the needle points N. With 

1 amp in the upper wire, the needle points NW. 



— >r-^ 



71 



STUDY GUIDE 



(a) What is the direction of this one ampere 
current? 

(b) What current (magnitude and direction) in 
the lower wire would restore the compass 
to its original position? 

14.30 The deflecting force on a charged particle 
moving perpendicularly to a uniform magnetic 
field is always perpendicular to its velocity vector, 
hence it is directed at every moment toward a 
single point — the center of the circular path the 
particle follows. 

(a) Knowing that the magnetic force (given by 
the expression qvB) therefore provides a 
centripetal force (which is always given by 
mv^lR), show that the radius of the circle 
R is directly proportional to the momentum 
of the particle mv. 

(b) What information would you need to 
determine the ratio of the particle's charge 
to its mass? 

14.31 By referring to the information given in 
the last problem: 

(a) Find an equation for the period of the 
circular motion of a charged particle in a 
uniform magnetic field. 

(b) Show mathematically that the radius of 
the helical path will be smaller where the 
magnetic field strength is greater. 

(c) Use the right hand rule to show that the 
direction of the deflecting force on the 
particle is such as to oppose the movement 
of the particle into the region of stronger 
field. 

14.32 If the energy of charged particles approach- 
ing the earth (say from the sun) is very great, 
they will not be trapped in the Van Allen belts, 
but rather they will be somewhat deflected, 
continuing on past or into the earth. The direction 
of the lines of force of the earth's magnetic field 
is toward the earth's north end. If you set up a 
detector for positively charged particles on the 
earth, would you expect to detect more particles 
by directing it slightly toward the east or slightly 
toward the west? 




14.33 William Gilbert in De Magnete recorded 
that a piece of amber that had been rubbed 
attracted smoke rising from a freshly extinguished 
candle, the smoke particles having been charged 
by passing through the ionized gases of the flame. 
After the development of electric machines, 
experiments were done on the discharges from 
sharp or pointed electrodes like needles, called 
corona discharges, and Hohlfeld found in 1824 
that passing such a discharge through a jar filled 
with fog, cleared the fog from the jar. A similar 
experiment was performed by Guitard only using 
tobacco smoke. The corona discharge in these 
experiments ionized the gas which in turn 
charged the water droplets of the fog or the 
smoke particles. 

However, no successful industrial precipitator 
came until Cottrell, using the electric generator, 
high voltage transformer, and mechanical 
rectifier developed in the last decades of the 
nineteenth century, achieved both a strong corona 
discharge and a high potential difference 
between the discharge electrode and the collect- 
ing electrode. Since that time many electrostatic 
precipitators have been built by electrical and 
chemical engineers to collect many kinds of 
particulate matter, the most important of which 
being fly ash from the burning of coal in the 
electrical power industry itself. 



<.xhausf jft^fts ujith- 




V 



characJ poi-'^icles art 
. dri'ven by dectvic -fi^ld 

tn+en5€- f'tlj n^or- uj<r^ 
ionizes <jajs , ujh,o^ t\i\/ts 

__r!eutiTxl parTi'cks ar«, 
OLttradTea 'to c€r'+f V wire 



Ac high vol+oae 



Suspended particiCS 



What are the implications of this technological 
development for control of pollution? Is it widely 
used? If not. why not? 




72 





A before-and-after example of the effect of electrostatic precipitators. The principle is 
described in SG 14,32 on the opposite page. 



73 



15.1 The problem: getting energy from one place to another 75 

15.2 Faraday's early work on electricity and lines of force 76 

15.3 The discovery of electromagnetic induction 77 

15.4 Generating electricity by the use of magnetic fields: the 
dynamo 81 

15.5 The electric motor 84 

15.6 The electric light bulb 86 

15.7 Ac verus dc, and the Niagara Falls power plant 90 

15.8 Electricity and society 94 




CHAPTER FIFTEEN 



Faraday and the Electrical Age 



15.1 The problem: getting energy from one place to another 

In Chapter 10 we discussed the development of the steam engine 
in the eighteenth and nineteenth centuries, which enabled Europe SG 15.1 

and America to make use of the vast stores of energy contained in 
coal, wood and oil. By burning fuel, chemical energy can be 
converted into heat energy. Then by using this heat energy to make 
steam and letting the steam expand against a piston or a turbine 
vane, heat energy can be converted to mechanical energy. In this 
way a coal-fueled steam engine can be used to run machinery. 

But steam engines suffered from two major defects; the 
mechanical energy was available only at the place where the 
steam engine was located, and practical steam engines were then 
big, hot, and dirty. As a result of the widespread use of machines 
run by steam engines, people were crowded together in factories, 
and their homes stood in the shadow of the smoke stacks. It was 
possible also to use steam engines for transportation by making 
locomotives; locomotives could be astonishing and powerful, but 
were limited by their size and weight (and added further to 
polluting the air). 

These defects in the practical use of steam power might be SG 15.2 

partially avoided by using one central power plant from which 
energy could be sent out, for use at a distance by machines of any 
desired size and power, at the most useful locations. After Volta's 
development of the battery, many scientists and inventors specu- 
lated that electricity might provide such a means of distributing 
energy and running machines. But the energy in batteries is 
quickly used up, unless it is delivered at a feeble rate. A better way 
of generating electric currents was needed. As we shall see, when 
this was found it changed the whole shape of life at home, in 
factories, on the farm, and in offices. And it changed also the very 
appearance of cities and landscapes. 

In this chapter we wOl see an example of how discoveries in 
basic physics have given rise to new technologies — technologies 

75 



76 



Faraday and the Electrical Age 



SG 15.3 



Ampere also sensed that electricity 
might transmit not only energy but 
also information to distant places. 



which have revolutionized and benefited modern civilization, 
though not without bringing some new problems in their turn. 

In retrospect, the first clue to the wide use of electricity came 
from Oersted's discovery that a magnetic needle is deflected by a 
current. A current can exert a force on a magnet; thus it was 
natural that speculations arose everywhere that somehow a magnet 
could be used to produce a current in a wire. (Such reasoning from 
symmetry is common in physics -and often is useful.) Within a few 
months after the news of Oersted's discovery reached Paris, the 
French physicists Biot, Savart, and Ampere had begun research on 
the suspected interactions of electricity and magnetism. (Some of 
their results were mentioned in Chapter 14.) A flood of other 
experiments and speculations on electromagnetism from all over 
the world was soon filling the scientific journals. Yet the one crucial 
discovery -the continuous and ample generation of electric current 
— still eluded everyone. 



15.2 Faraday's early work on electricity and lines of force 

A valuable function of scientific journals is to provide for their 
readers comprehensive survey articles on recent advances in 
science, as well as the usual more terse announcements of the 
technical details of discoveries. The need for a review article is 
especially great after a large burst of activity such as that which 
followed Oersted's discovery of electromagnetism in 1820. 

In 1821 the editor of the British journal Annals of Philosophy 
asked Michael Faraday to undertake a historical survey of the 
experiments and theories of electromagnetism which had appeared 
in the previous year. Faraday, who had originally been apprenticed 
to a bookbinder, was at that time an assistant to the well-known 
chemist Humphry Davy. Although Faraday had no formal training 
in science or mathematics, he was eager to learn all he could. He 
agreed to accept the assignment, but soon found that he could not 
limit himself merely to reporting what others had said they had 
done. He felt he had to repeat the experiments in his own laboratory, 
and, not being satisfied with the theoretical explanations proposed 
by other physicists, he started to work out his own theories and 
plans for further experiments. Before long Faraday launched a 
series of researches in electricity that was to make him one of the 
most famous physicists of his time. 

Faraday's first discovery in electromagnetism was made on 
September 3, 1821. Repeating Oersted's experiment (described in 
Sec. 14.11), he put a compass needle at various places around a 
current-carrying wire. Faraday was particularly struck by the fact 
that the force exerted by the current on each pole of the magnet 
would tend to carry the pole along a circular line around the wire. 
As he expressed it later, the wire is surrounded by circular lines 
offeree or a circular magnetic field. Faraday then constructed an 
"electromagnetic rotator" based on this idea. It worked. Though 
very primitive, it was the first device for producing continuous 
motion owing to the action of a current — the first electric motor. 



Section 15.3 



77 



Faraday also designed an arrangement in which the magnet 
was fixed and the current-carrying wire rotated around it. (If a 
current can exert a force on a magnet, a magnet should be able to 
exert an equal force on a current, according to Newton's third law.) 
As in many other cases, Faraday was guided by the idea that for 
every effect of electricity on magnetism, there must exist a converse 
effect of magnetism on electricity — though it was not always so 
obvious what form the converse effect would take. 

Q1 Why is the magnetic pole of Faraday's "electromagnetic 
rotator" pushed in a circle around a fixed wire? 



15.3 The discovery of electromagnetic induction 

Armed with his "lines of force" picture for visualizing electric 
and magnetic fields, Faraday joined in the search for a way of 
producing currents by magnetism. Scattered through his diary in 
the years after 1824 are many descriptions of such experiments. 
Each report ended with a note: "exhibited no action" or "no effect." 

Finally, in 1831, came the breakthrough. Like many discoveries 
which have been preceded by a period of preliminary research and 
discussion among scientists, this one was made almost simultane- 
ously by two scientists working independently in different countries. 
Faraday was not quite the first to produce electricity from 
magnetism; electromagnetic induction, as it is now called, was 
actually discovered first by an American scientist. Joseph Henry. 
Henry was teaching mathematics and philosophy at an academy 
in Albany, New York, at the time. Unfortunately for the reputation 
of American science, teachers at the Albany Academy were expected 
to spend all their time on teaching and administrative duties, with 
no time left for research. Henry had hardly any opportunity to follow 
up his discovery, which he made during a one-month vacation. He 
was not able to publish his work until a year later; and in the 
meantime Faraday had made a similar discovery and published 
his results. 

Faraday is known as the discoverer of "electromagnetic 
induction" (production of a current by magnetism) not simply 
because he established official priority by first publication, but 
primarily because he conducted exhaustive investigations into all 
aspects of the subject. His earlier experiments and his ideas about 
lines of force had suggested the possibility that a current in one 
wire ought somehow to be able to induce a current in a nearby wire. 
Oersted and Ampere had shown that a steady electric current 
produced a steady magnetic field around the circuit carrying the 
current. One might think that a steady electric current could 
somehow be generated if a wire were placed near or around a 
magnet, although a very strong magnet might be needed. Or a 
steady current might be produced in one wire if a very large steady 
current exists in another wire nearby. Faraday tried all these 
possibilities, with no success. 




Two versions of Faraday s electro- 
magnetic rotator. In each, the cup was 
filled with mercury so that a large cur- 
rent can be passed between the base 
and overhead support. 





In one version (left) the north end of a 
bar magnet revolves along the circular 
electric lines of force surrounding the 
fixed current. In the other version 
(right), the rod carrying the current 
revolves around the fixed bar magnet 
— moving always perpendicular to the 
magnetic lines of force coming from 
the pole of the magnet. 




Michael Faraday (1791-1867) was 
the son of an English blacksmith. 
In his own words: 

My education was of the most 
ordinary description, consisting 
of little more than the rudiments 
of reading, writing and arithmetic 
at a common day-school. My hours 
out of school were passed at home 
and in the streets. 

At the age of twelve he went to work 
as an errand boy at a booksellers 
store. Later he became a book- 
binder s assistant. When Faraday 
was about nineteen he was given a 
ticket to attend a series of lectures 
given by Sir Humphry Davy at the 
Royal Institution in London. The 
Royal Institution was an important 
center of research and education in 
science, and Davy was Superintendent 
of the Institution. Faraday became 
strongly interested in science and 
undertook the study of chemistry by 
himself. In 1813. he applied to Davy 
for a job at the Royal Institution and 
Davy hired him as a research 
assistant. Faraday soon showed 
his genius as an experimenter. He 
made important contributions to 
chemistry, magnetism, electricity 
and light, and eventually succeeded 
Davy as superintendent of the Royal 
Institution. 

Because of his many discoveries. 
Faraday is generally regarded as one 
of the greatest of all experimental 
scientists. Faraday was also a fine 
lecturer and had an extraordinary 
gift for explaining the results of 
scientific research to non-scientists. 
His lectures to audiences of young 
people are still delightful to read. 
Two of them. On the Various Forces 
of Nature and The Chemical 
History of a Candle." have been 
republished in paperback editions. 

Faraday was a modest, gentle 
and deeply religious man. Although 
he received many international 
scientific honors, he had no wish 
to be knighted, preferring to remain 
without title. 



Faraday's laboratory at the Royal Institution. 



Section 15.3 



79 









^ 






0/^ 



4C j^.^cu- r^^-^ ^..Jdir^A^ ^ 









J" 



* .y/^ ..~*x z-;^ / 1 ^^^-^ ^ Jj^ 

The solution Faraday found in 1831 came in good part by 
accident. He was experimenting with two wire coils that had been 
wound around an iron ring (see illustration in the margin). He 
noted that a current appeared in one coil only while the current in 
the other coil was being switched on or off. When a current was 
turned on in coil A, a current was indeed induced in coil B, but 
it lasted only for a moment. As soon as there was a steady current 
in the coil A, the current in the coil B disappeared. But when the 
current in the coil A was turned off, again there was a momentary 
current induced in coil B. 

To summarize Faraday's result: a current in a stationary wire 
can induce a current in another stationary wire only while it is 
changing. But a steady current in one wire cannot induce a current 
in another wire. 

Faraday was not satisfied with merely observing and reporting 
this curious and important result. Guided by his concept of "lines 
of force," he tried to find out what were the essential factors 
involved in electromagnetic induction, as distinguished from the 
merely accidental arrangement of his first experiment. 

According to Faraday's theory, the changing current in coil A 
would change the lines of magnetic force in the whole iron ring, 
and that change in lines of magnetic force in the part of the ring 
near coil B would induce a current in B. But if this was really the 
correct explanation of induction, Faraday asked himself, shouldn't 
it be possible to produce the same effect in another way? In 
particular: 

1. Is the iron ring really necessary to produce the induction 
effect, or does the presence of iron merely intensify an effect that 
would also occur without it? 



Part of a page in Faraday's diary where 
he recorded the first successful exper- 
iment in electromagnetic induction, 
August 29, 1831. (About factual size.) 




.s: 



i(^ 



80 



Faraday and the Electrical Age 






SG 15.4 
SG 15.5 




2. Is coil A really necessary, or could current be induced merely 
by changing the magnetic lines of force through coil B in some 
other way. such as by moving a simple magnet relative to the wire? 

Faraday answered these questions almost immediately by 
further experiments. First, he showed that the iron ring was not 
necessary; starting or stopping a current in one coil of wire would 
induce a momentary current in a nearby coil with only air (or 
vacuum) between the coils. (See top figure at the left) Second, he 
found that when a bar magnet was inserted into or removed from a 
coil of wire, a current was induced at the instant of insertion or 
removal. (See second figure at the left) In Faraday's words. 

A cylindrical bar magnet . . . had one end just inserted 
into the end of the helix cylinder; then it was quickly 
thrust in the whole length and the galvanometer needle 
moved; then pulled out again the needle moved, but in 
the opposite direction. The effect was repeated every time 
the magnet was put in or out .... 

Note that this is a primitive electric generator: it provides electric 
current by having some mechanical agent move a magnet. 

Having done these and many other experiments. Faraday stated 
his general principle of electromagnetic induction: changing lines 
of magnetic force can cause a current to be generated in a wire. 
The needed "change" in lines of force can be produced either by 
(a) a magnet moving relative to a wire (Faraday found it convenient 
to speak of wires "cutting across" lines of force) or (b) a changing 
current (in which case the lines of force changing would "cut 
across" the wire). He later used the word field to refer to the 
arrangement and intensity of lines of force in space. We can say, 
then, that a current can be induced in a circuit by variations in a 
magnetic field around the circuit. Such variations may be caused 
either by relative motion of wire and field, or just by the change in 
intensity of the field. 

So far Faraday had been able to produce only momentary 
surges of current by induction. That of course would hardly be an 
improvement over batteries as a source of current. Is it possible 
to produce a continual current by electromagnetic induction? To do 
this one has to create a situation in which magnetic lines of force 
are continually changing relative to the conductor. If a simple 
magnet is used, the relative change can be produced either by 
moving the magnet or by moving the conductor. This is just what 
Faraday did: he turned a copper disk between the poles of a magnet. 
(See illustration in margin.) A steady current was produced in a 
circuit connected to the disk through brass brushes. This device 
(called the "Faraday disk dynamo") was the first constant-current 
electric generator. Although this particular arrangement did not 
turn out to be very practical, at least it showed that continuous 
generation of electricity was possible. 

These first experimental means of producing a continuous 
current were important not only for clarifying the connection 
between electricity and magnetism; they also suggested the 



Section 15.4 



81 



possibility of generating electricity eventually on a large scale. The 
production of electrical current involves changing energy from one 
form to another. When electrical energy appears, it is at the cost of 
some other form of energy; in the electric battery, chemical energy 
— the energy of formation of chemical compounds — is converted 
into electrical energy. Although batteries are useful for many 
portable applications (automobiles and flashlights for example) it 
is not practical to produce large amounts of electrical energy by 
this means. There is, however, a vast supply of mechanical energy 
available from many sources that could produce electrical energy 
on a large scale if some reasonably efficient means of converting 
mechanical energy into electrical energy were available. This 
mechanical energy may be in the form of wind, or water falling 
from high elevation, or continuous mechanical motion produced, 
for example, by a steam engine. The discovery of electromagnetic 
induction showed that, at least in principle, it was feasible to 
produce electricity by mechanical means. In this sense Faraday can 
rightly be regarded as initiating the modern electrical age. 

But, although Faraday realized the practical importance of his 
discoveries, his primary interest was in basic science, the search 
for laws of nature and for a deeper understanding of the relation- 
ship between the separate experimental and theoretical findings. 
Though he appreciated the need for applied science, such as the 
eventual perfection of specific devices, he left the development of 
the generator and the motor to others. On the other hand, the 
inventors and engineers who were interested in the practical and 
profitable applications of electricity at that time did not know much 
about physics, and most of the progress during the next fifty years 
was made by trial and error. In following the development of 
modern electrical technology, as a case study in the long range 
effects of scientific work, we will see several problems that could 
have been solved much earlier if a physicist with Faraday's 
knowledge had been working on them. 

Q2 Why is Faraday considered the discoverer of electro- 
magnetic induction? 

Q3 What is the general definition of electromagnetic 
induction? 



15.4 Generating electricity by the use of magnetic fields: the dynamo 

Faraday had shown that when a conducting wire moves relative 
to a magnetic field, a current is produced. Whether it is the wire or 
the magnetic field that moves doesn't matter; what counts is the 
relative motion of one with respect to the other. Once the principle 
of electromagnetic induction had been discovered, the path was 
open to try all kinds of combinations of wires and magnets in 
relative motion. We shall describe one basic type of generator (or 
"dynamo," as it was often called) which was frequently used in 
the nineteenth century and which is still the basic model for 
many generators today. 




One generator of 1832 had a perma- 
nent horseshoe magnet rotated by 
hand beneath two stationary coils. 



82 



Faraday and the Electrical Age 



Alternating-current generator. 




^ 




This form of generator is basically a coil of 
wire that can be rotated in a magnetic field. The 
coil is connected to an external circuit by sliding 
contacts. In the diagram on the left, the "coil"" 
made for simplicity out of a single rectangular 
loop of wire is made to rotate around an axis XY 
between the north and south poles of a magnet. 
Two conducting rings d and e are permanently 
attached to the loop, and therefore, also rotate 
around the axis; conducting brushes /and g are 
provided to complete a circuit through a meter 
at h that indicates the current produced. The 
complete circuit is abdfhgea. (Note that the wire 
goes from a through ring d without touching it 
and connects to e.) 

Initially the loop is at rest, and no charge 
flows through it. Now suppose we start to rotate 
the loop. The wire's long sides a and b will have 
a component of motion perpendicular to the 
direction of the magnetic lines of force; that is, 
the wire "cuts across" lines of force. This is the 
condition for an electric current to be induced in 
the loop. The greater the rate at which the lines 
are cut, the greater the induced current is. 

Now, to get a better understanding of what is 
going on in the wire, we will describe its operation 
in terms of force on the charges whose move- 
ment constitutes the current. Because the 
charges in the part of the loop labeled b are 
being physically moved together with the loop 
across the magnetic field, they experience a 
magnetic force given by qvB (as described in 
Sec. 14.13). As a consequence these charges in 
the wire will be pushed "off to the side" by the 



Section 15.4 



83 




magnetic field through which they are moving; 
"off to the side" in this situation is along 
the wire. 

What about side a? That side of the loop is 
also moving through the field and "cutting" lines 
of force, but in the opposite direction. So the 
charges in a experience a push along the wire 
in the opposite direction compared to those in b. 
This is just what is needed; the two effects 
reinforce each other in generating a current 
around the whole loop. 

The generator we have just described produces 
what is called alternating current (abbreviated 
ac), because the current periodically reverses 
(alternates) its direction. At the time this kind of 
generator was first developed, in the 1830's, alter- 
nating current could not be used to run machines. 
Instead, direct current (dc) was desired. 

In 1832, Ampere announced that his 
instrument-maker, Hippolyte Pixii, had solved 
the problem of generating direct current. Pixii 
modified the ac generator by means of an 
ingenious device called the commutator (from 
the word commute, to interchange, or to go back 
and forth). The commutator is a split cylinder 
inserted in the circuit so that the brushes /and 
g, instead of always being connected to the same 
part of the loop, as in the previous figure, reverse 
connections each time the loop passes through 
the vertical position. Just as the direction of 
current induced in the loop is at the point of 
reversing, the contacts reverse; as a result, the 
current in the outside circuit is always in the 
same direction. 



Direct-current generator. 




\COKI!£Jjr 



—^ ^TiHIt, 



cs Jl 




84 



Faraday and the Electrical Age 



SG 15.6 



The current continually reverses 
direction so, in one sense, the 
average value for / is zero; charge 
is moved back and forth in the wire, 
but not transferred through it. P is 
always positive, however. 



SG 15.7-15.9 



Although the current in the outside circuit is always in the 
same direction, it is not constant, but fluctuates rapidly between 
zero and its maximum value, as shown in the marginal drawings 
on page 83. Many sets of loops and commutators are connected 
together on the same shaft in such a way that their induced 
currents reach their maximum and zero values at different times; 
the total current from all of them together is then more uniform. 

Whether a generator delivers alternating or direct current (ac 
or dc), the electric power (energy per unit time) it produces at every 
instant is given by the same equation we developed in Sec. 14.10. 
For example, suppose that a wire (for example, the filament wire 
in a light bulb) with resistance R is substituted for the meter (at h). 
If the current generated in the circuit at a given time is I. the 
electrical energy per unit time delivered to the wire is given by 
PR. For alternating current, the power output varies from instant 
to instant, but the average output power is simply {r-)^yR. This 
electrical energy of course does not appear by itself, without any 
source of energy; that would violate the laws of conservation of 
energy. In our generator, the "source" of this energy is of course 
the mechanical energy that must be provided to the rotating shaft 
to keep the coils rotating in the magnetic field. This mechanical 
energy is provided by a steam or gasoline engine, or by water power, 
wind power, etc. The generator is thus a device for converting 
mechanical to electrical energy. 

Q4 What is the position of a rotating loop when it generates 
maximum current? minimum? Why? 

Q5 What is the purpose of the commutator? 

Q6 Where does the energy delivered by the generator come 
from? 



15.5 The electric motor 

The biggest initial obstacle to the use of motors was the 
difficulty of providing cheap electric cuiTent to run the motor. The 
chemical energy in batteries was quickly exhausted. The dynamo, 
invented almost, simultaneously by Faraday and Henry in 1832. 
was at first no more economical than the battery. It was only 
another "philosophical toy." Design of electric generators that used 
mechanical power to produce electrical power depended on under- 
standing the details of operation, and this took nearly 50 years. 
The intervening period was one of numerous inventions that 
aroused great temporary enthusiasm and ambitious plans, followed 
by disillusion resulting from unanticipated practical difficulties. 
But the hope of a fortune to be made by providing cheap power to 
the world spurred on each new generation of inventors, and 
knowledge about the physics and technology of electromagnetic 
systems gradually accumulated. 

In fact, it was a chance event that marks the beginning of the 
electric power age- an accidental discoven' at the Vienna Exhibition 



Section 15.5 



85 



of 1873. It is of course not quite accurate to ascribe the beginnings 
of an era to one man, in one place, performing one act, at one time. 
In reality, with many men thinking about and experimenting in a 
particular scientific field, what does happen is that the situation 
becomes favorable for a breakthrough, and sometimes a seemingly 
trivial chance event is all that is needed to get things going. In this 
case, as the story goes, an unknown workman at the exhibition just 
happened to connect two dynamos together. The current generated by 
one dynamo went through the coils of the other dynamo which then 
ran as an electric motor on the electricity generated by the first. 





This accidental discovery, that a generator could be used to 
function as a motor, was immediately utilized at the exhibition in 
a spectacular public demonstration: a small artificial waterfall was 
used to drive the generator. Its current then drove the motor, which 
in turn operated a pump to spray water from a fountain. Thus 
electromagnetic induction was first used to convert mechanical 
energy into electrical energy by means of a generator; the electrical 
energy could be transmitted over a considerable distance and 
converted back into mechanical energy by a motor. This is the basic 
operation of a modern electrical transmission system: a turbine 
driven by steam or falling water drives a generator which converts 
the mechanical energy to electrical energy; conducting wires 
transmit the electricity over long distances to motors, toasters, 
electric hghts, etc., which convert the electrical energy to mechani- 
cal energy, heat or light. 

The development of electrical generators shows the interaction 
of science and technology in a different light than did the develop- 
ment of steam engines. As was pointed out in Chapter 10, the early 
steam engines were developed by practical inventors who had no 
knowledge of what we now consider to be the correct theory of 
heat (thermodynamics). In fact, it was the development of the 
steam engine and attempts by Sadi Carnot and others to improve 
its efficiency through theoretical analysis, that was one of the major 
historical factors leading to the estabhshment of thermodynamics. 
In that case, the advance in technology came before the advance in 
science. But in the case of electromagnetism a large amount of 
scientific knowledge was built up by Ampere, Faraday, Kelvin and 
Maxwell before there was any serious success in practical applica- 
tion. The scientists who understood electricity better than anyone 
else were not especially interested in commercial applications, and 
the inventors who hoped to make huge profits from electricity knew 
very httle of the theory. Although after Faraday announced his 
discovery of electromagnetic induction people started making 
generators to produce electricity immediately, it was not until 40 



4?«ife 



SG 15.10, 15.11 




Assembling a commercial generator. 
As in almost all large generators, the 
coils of wire in which current is in- 
duced are around the outside, and 
electromagnets are rotated on the 
inside. 



86 



Faraday and the Electrical Age 




Water-driven electric generators pro- 
ducing power at the Tennessee Valley 
Authority. The plant can generate 
electric energy at a rate of over 
100,000,000 watts. 



years later that inventors and engineers became sufficiently familiar 
with such necessary concepts as lines of force and field vectors. 
With the introduction of the telegraph, telephone, radio and 
alternating-current power systems, the amount of mathematical 
knowledge needed to work with electricity became quite large. 
and universities and technical schools started to give courses in 
electrical engineering. In this way there developed a group of 
specialists who were familiar with the physics of electricity and 
also knew how to apply it. 

Q7 How would you make an electric motor out of a generator? 

Q8 What prevented the electric motor from being an immediate 
economic success? 

Q9 What chance event led to the beginning of the electric 
power age? 



15.6 The electric light bulb 

The growth of the electric industry has been largely due to the 
public demand for electrical products. One of the first of these to 
be commercially successful in the United States was the electric 
light bulb. It is an interesting case of the interrelation between 
physics, industry and society. 



Section 15.6 



87 



At the beginning of the nineteenth century, illumination for 
buildings and homes was provided by candles and oil lamps. Street 
lighting in cities was practically nonexistent, in spite of sporadic 
attempts to hang lights outside houses at night. The natural gas 
industry was just starting to change this situation, and the first 
street lighting system for London was provided in 1813 when gas 
lights were installed on Westminster Bridge. However, the introduc- 
tion of gas lighting in factories was not entirely beneficial in its 
social effects, since it enabled employers to extend an already long 
and difficult working day into a longer one still. 

In 1801. the British chemist Humphry Davy noted that a 
brilliant spark or arc appeared when he broke contact between two 
carbon rods which were connected to the two terminals of a 
battery. This discovery led to the development of the "arc light." 

The arc light was not practical for general use until the steam- 
driven electrical generators had replaced expensive batteries as a 
source of electric current. In the 1860's and 1870's, arc lights began 
to be used for street lighting and lighthouses. However, the arc light 
was too glaring and too expensive for use in the home. The carbon 
rods burned up in a few hours because of the high temperatures 
produced by the arc. and the need for frequent service and replace- 
ment made this system inconvenient. (Arc lights are still used for 
some high intensity purposes such as spotlights in theaters.) 

As Humphry Davy and other scientists showed, light can be 
produced simply by producing a current in a wire (often called a 
filament) to heat it to a high temperature. This method is known 
as incandescent lighting. The major technical drawback was that 
the material of the filament gradually burned up. The obvious 
solution was to enclose the filament in a glass container from 
which all the air had been removed. But this was easier said than 
done. The vacuum pumps available in the early nineteenth century 
could not produce a sufficiently good vacuum for this purpose. It 
was not until 1865, when Hermann Sprengel in Germany invented 
an exceptionally good vacuum pump, that the electric light bulb 
in its modern form could be developed. (The use of Sprengel's pump 
by Crookes and others was also vital in scientific experiments 
leading to the discoveries in atomic physics which we will discuss 
in Chapter 18.) 

Thomas Edison was not the first to invent an incandescent 
light using the Sprengel pump, nor did he discover any essentially 
new scientific principles. What he did was develop a light bulb 
which could be used in homes, and (even more important) a 
distribution system for electricity. His system not only made the 
light bulb practical but also opened the way for mass consumption 
of electrical energy in the United States. 

Edison started from the basic assumption that each customer 
must be able to turn on and off his own light bulbs without affecting 
the other bulbs connected to the circuit. This meant that the bulbs 
must be connected "in parallel" — like the rungs of a ladder rather 
than "in series." 




Davy's arc lamp 




Demonstrations of the new electric 
light during a visit of Queen Victoria 
and Prince Albert to Dublin, Ireland. 
From Illustrated London News. Au- 
gust 11, 1849. 




In the late 1800's, dynamo powered 
arc-lamps were used in some Euro- 
pean cities. 



Thomas Alva Edison (1847-1931) was 
born at Milan, Ohio, and spent most 
of his boyhood at Port Huron, 
Michigan. His first love was 
chemistry, and to earn money for 
his chemical experiments, he set up 
his own business enterprises. Before 
he was fifteen, he ran two stores in 
Port Huron, one for periodicals and 
the other for vegetables; hired a 
newsboy to sell papers on the Grand 
Trunk Railway running between Port 
Huron and Detroit; published a 
weekly newspaper; and ran a 
chemical laboratory in the baggage 
car of the train. His financial empire 
was growing rapidly when, in 1862, 
a stick of phosphorus in his labora- 
tory caught fire and destroyed part 
of the baggage car. As a result, his 
laboratory and newspaper equipment 
were evicted from the train, and he 
had to look for another base of 
operations. 

it was not long before his bad 
luck with the phosphorus was offset 
by a piece of good luck: he was able 
to save the life of the son of the 
station agent by pulling him out of 
the path of an oncoming train. In 
gratitude, the station agent taught 
Edison the art of telegraphy, and 
thus began Edison's career in 
electricity. 

At the right are shown two 
portraits of Edison. On the opposite 
page is a copy of the drawing that 
accompanied his patent on the 
incandescent lamp. The labeled parts 
are the carbon filament (a), thickened 
ends of filament (c), platinum wires 
(d), clamp (h), leading wires (x), 
copper wires (e), tube to vacuum 
pump (m). 




\^ ■ - V' 




Section 15.6 



89 



The choice of parallel rather than series circuits — a choice 
based on the way Edison thought the consumer would want to 
use the system — had important technical consequences. In a series 
circuit, the same current would go through each bulb. In a parallel 
circuit, only part of the total current available from the source goes 
through any one bulb. To keep the total current needed from being 
too large, the current in each bulb would have to be small. 

As was pointed out in Chapter 14, the heating effect of a current 
depends on both the resistance of the wire and the amount of 
current it carries. The rate at which heat energy is produced is 
PR; that is, it goes up directly as the resistance, but increases as 
the square of the current. Therefore, most inventors used high- 
current, low-resistance bulbs, and assumed that parallel circuits 
would not be practical. But Edison realized that a small current 
can have a large heating effect if the resistance is high enough. 

So Edison began a search for a suitable high-resistance, 
non-metallic substance for his filaments. To make such a filament, 
he first had to bake or "carbonise" a thin piece of a substance; then 
he would seal it inside an evacuated glass bulb with wires leading 
out. His assistants tried more than 1,600 kinds of material: "paper 
and cloth, thread, fishline, fiber, celluloid, boxwood, coconut-shells, 
spruce, hickory, hay. maple shavings, rosewood, punk, cork, flax, 
bamboo, and the hair out of a redheaded Scotchman's beard." His 
first successful high-resistance lamp was made with carbonized 




Series circuit 



SG 15.12, 15.13 

See the article The Invention of 
the Electric Light" in Reader 4. 



T. A. EDISON. 
Electric-Lamp. 

No. 223,898. Patented Jan. 27. 1880. 



%' •'■' 




fmmiua 



"^'^, 



ChwvrUbt 

She I nan U (cditorv 




One type of Edison lamp. Note the 
familiar filament and screw-type base. 



Drawing (about \ size) that accom- 
panied Edison's patent application. 



90 



Faraday and the Electrical Age 



■S LIGHT. 



Tiie Great Inventor's Triurapli in 
Electric Illnmination. 



A SCRAP OF PAPER. 



It Makes a Light, "Witbout Gas or 
Flame, Cheaper Than Oil. 



Wimm IN THE Fl'RNAGE. 



Complete Details of the Perfected 
Carbon Lamp. 



FIFTEEN MONTHS OF TOIL. 



S:oiy of His Tireless ExpcnmeDts wilh Lamps, 
B'jriiers and Gscerators. 



SUCCESS IN A COTTON THREAD. 



The Wizard's Byplay, with Eodily Pain 
amd Gold "Tailings." 



HISTORY OF ELECTRIC LIGHTING. 



Tuc otAT approacb of ibe first puullc exhibition of 
fi-iiscD's lou^ looked for electric llf^lit, knoouuced tu 
like place OD »<r Vear'a Eve >t Moolo Perk, od 
^Uicli occAiUou tlisl p:ace will U) lUuuiLnftteti Witt 
tbe Dew h^ht, hae reTivi.d public iutcreot iii the 
great lUTector's Tork, and tbrougbout the civilised 
vurlU Bcientiets and people geoerftlly ere auuously 
>«-aiUuK tbe result. Froio tbo brginniiig of bie ei- 
pcr^meiita lo electric ll^btiDg to the preeeut time 
^r. Edisoa b.4B kept bin Ubor.itorjr ga:irdodly 
clu»cJ, and DO aulbontatire accouut (except tbat 
pukb-ibeJ Id the UEKaLD eomo moctus ago routine 

10 bie flrdt paiciit) of any of tbo luiportant 6U^\>a of 

bii progrcaa baa bcca made public — a courao of pro- 

ctJure tbo mreulor found abaolately noceaearj' for 

bis owo ptotecllon. Tbo Ucitau> !• now, bowevor. 

euAbled to present to Its readers a full and accurate 

account of his work from Us loceptlon to Its com- 

Ileiion. 

a LJuinu) ParrJi. 

E.lUou's electrtc llgbl, lucrsdable aa it may appear. 

11 produced from a little picco of paper— a tiny strip 
of oaper that a breath wonld blow away. Tbroni:b 



First newspaper account of Edison's 
invention (New York Herald, Decem- 
ber 21. 1879). 



cotton thread, enclosed in a high-vacuum sealed bulb. It burned 
continuously for two days before it fell apart. This was in October 
1879. The following year, Edison produced lamps with filaments 
made from Bristol board, bamboo, and paper. 

The Edison Electric Light Company began to install lighting 
systems in 1882. After only three years of operation, the Edison 
company had sold 200,000 lamps. It had a virtual monopoly of the 
field, and began to pay handsome dividends to its stockholders. 

The electric light bulb had undergone some modification since 
Edison's original invention. For example, the carbonized filaments 
of the older lamps have been replaced in newer bulbs by a thin 
wire of tungsten, which has the advantages of greater efficiency 
and longer life. 

The widespread use of light bulbs (confirming the soundness 
of Edison's theory about what people would buy) led to the rapid 
development of systems of power generation and distribution. The 
need for more power for lighting spurred the invention of better 
generators, the replacement of direct harnessing of water power, 
and the invention of the steam turbine. Then, success in providing 
larger quantities of energy at lower cost made other uses of 
electricity practical. Once homes were wired for electric lights, 
the current could be used to run sewing machines, vacuum 
cleaners, washing machines, toasters, and (later on) refrigerators, 
freezers, radios and television sets. Moreover, once electric power 
was available for relatively clean public transportation, cities would 
grow rapidly in all dimensions -through elevators that made high- 
rise buildings practical, and through electric tramways and subways 
that provided people rapid transporation from their homes to their 
jobs and to markets. 

We have now become so accustomed to the more sophisticated 
and spectacular applications of electricity that it is hard to realize 
the impact of something as simple as the electric light bulb. But 
most people who lived through the period of electrification — for 
example, in the 1930s and 1940's in many rural areas of the United 
States -agreed that the one single electrical appliance that made 
the greatest difference in their own daily lives was the electric 
Hght bulb. 

Q10 Why were arc lights not used for illuminating homes? 

Q11 What device was essential to the development of the 
incandescent lamp? 

Q12 Why did Edison require a substance with a high resistance 
for his light bulb filaments? 

Q13 What were some of the major effects the introduction of 
electric power had on everyday life? 

15.7 Ac versus do, and the Niagara Falls power plant 

In Sec. 15.5 we stated that the usual form of electric generator 
produces alternating current, but that it can be changed into direct 



Section 15.7 



91 



current by the use of a commutator. The reason for converting ac 
into dc was the general behef among practical engineers, held 
throughout most of the nineteenth century, that only dc was useful 
in the applications of electricity. However, as the demand for 
electric power increased, some of the inherent disadvantages of 
dc became evident. One disadvantage was the fact that the 
commutator complicated the mechanical design of the generator, 
especially if the ring had to be rotated at high speed. This difficulty 
was even more serious after the introduction of steam turbines in 
the 1890's, since turbines work most effectively when run at high 
speeds. Another disadvantage was the fact that there was no 
convenient way to change the voltage of direct current. 

One reason for wanting to change the voltage which drives 
the current in a transmission system involves the amount of power 
lost in heating the transmission wires. The power output of a 
generator depends, as we showed in Sec. 14.10, on the output 
voltage of the generator as well as on the amount of current: 

The same total power can be transmitted with smaller / if V is 
larger. Now, when there is a current I in a transmission wire of 
resistance R, the amount of power expended as heat in the 
transmission wires is proportional to the resistance and to the 
square of the current: 

"heat loss ~ 1 K. 

The power finally available to consumers is Ptotai — f*heat loss- This 
means that for transmission lines of a given resistance R. one 
wants to make the current I as small as possible in order to 
minimize the power loss in transmission. Obviously, therefore, 
electricity should be transmitted at low current and at high voltage. 

On the other hand, for most of the applications of electricity, 
especially in homes, it is neither convenient nor safe to use high 
voltages. Also, most generators cannot produce electricity at very 
high voltages (which would require excessively high speeds of the 
moving parts). Therefore we need some way of "stepping up" the 
electricity to a high voltage for transmission, and some way of 
"stepping it down" again for use at the other end. where the 
consumer uses the power. In short, we need a transformer. 

A transformer can easily be made by a simple modification of 
Faraday's induction coil (Sec. 15.4). Faraday was able to induce a 
current in a coil of wire (which we call the secondary coil) by 
winding this coil around one side of an iron ring, and then changing 
a current in another coil (the primary coil) which is wound around 
the other side of the ring. A cunent is induced in the secondary 
coil when the primary current changes. If the primary current is 
changing all the time, then a current will continually be induced 
in the secondary — an alternating current in the primary coil (as 
from a generator without a commutator) will induce an alternating 
current in the secondary coil. 



SG 15.14 




A steady current (dc) in the primary 
induces no current at all in the 
secondary; transformers work on ac. 



92 Faraday and the Electrical Age 

We need just one additional fact to make a useful electric 
transformer: if the secondary has more turns than the primary, the 
alternating voltage produced across the secondary coil will be 
greater than across the primary; if the secondary has fewer turns 
than the primary, the alternating voltage produced across the 
SG 15.15-15.17 secondary will be lower than the voltage across the primary. This 

fact was discovered by Joseph Henry, who built the first trans- 
former in 1838. 

The first ac system was demonstrated in Paris in 1883. An 
experimental line which powered arc and incandescent lighting, 
through transformers, was installed in a railway line in London in 
1884, and another one shortly afterward in Italy. An American 
engineer, George Westinghouse, saw the system exhibited in Italy 
and purchased the American patent rights for it. Westinghouse had 
already gained a reputation by his invention of the railway air brake, 
and had set up a small electrical engineering company in Pittsburgh 
in 1884. After making some improvements in the design and con- 
struction of transformers, the Westinghouse Electric Company set 
up its first commercial installation to distribute alternating current 
for incandescent lighting in Buffalo. New York, in 1886. 

At the time of the introduction of the Westinghouse ac system 
in the United States, the Edison Electric Light Company held 
almost a complete monopoly of the incandescent lighting business. 
The Edison Company had invested large amounts of money in 
providing dc generating plants and distribution systems for most 
of the large cities. Naturally Edison was alarmed by a new 
company which claimed to produce the same kind of electric power 
for illumination with a much cheaper system. There was a bitter 
public controversy, in which Edison attempted to show that ac is 
unsafe because of the high voltage used for transmission. In the 
middle of the dispute, the New York State Legislature passed a law 
establishing electrocution as a means of capital punishment, and 
this seems to have helped in arousing some of the popular fear 
SG 15.18 of high voltage. 

Nevertheless, the Westinghouse system continued to grow, and 
since there were no spectacular accidents, the public accepted ac 
as being reasonably safe. The invention of the "rotary converter" 
(essentially an ac motor driving a dc generator) made it possible to 
convert ac into dc for use in local systems already set up with dc 
equipment, or to power individual dc motors. Consequently the 
Edison company (later merged into General Electric) did not have 
to go out of business when ac was generally adopted. 

The final victory of the ac system was assured in 1893, when 
the decision was made to use ac for the new hydroelectric plant at 
Niagara Falls. In 1887, businessmen in Buffalo had pledged 
SIOO.OOO to be offered as a prize "to the Inventors of the World" 
who would design a system for utilizing the power of the Niagara 
River "at or near Buffalo, so that such power may be made prac- 
tically available for various purposes throughout the city. " The 
contest attracted world-wide attention, not only because of the 
large prize but also because large quantities of electrical power 



Section 15.7 93 

had never before been transmitted over such a distance — it was 
20 miles from Niagara Falls to Buffalo. The success or failure of 
this venture would influence the future development of electrical 
distribution systems for other large cities. 

It was a close decision whether to use ac or dc for the Niagara 
Falls system. The demand for electricity in 1890 was mainly for 
lighting, which meant that there would be a peak demand in the 
evening; the system would have to operate at less than full capacity 
during the day and late at night. Some engineers proposed that, 
even though ac could be generated and transmitted more efficiently, 
a dc system would be cheaper to operate if there were much 
variation in the demand for electricity. This was because batteries 
could be used to back up the generators in periods of peak demand. 
Thomas Edison was consulted, and without hesitation he recom- 
mended dc. But the Cataract Construction Company, which had 
been formed to administer the project, delayed making a decision. 

The issue was still in doubt in 1891 when, at the International 
Electrical Exhibition in Frankfort, Germany, an ac line carrying 
sizable quantities of power from Frankfort to Lauffen (a distance 
of 110 miles) was demonstrated. Tests of the line showed an 
efficiency of transmission of 77%. That is, for every 100 watts fed 
in at one end of the line, only 23 were wasted by heating effects in 
the line, and the other 77 were delivered as useful power. The 
success of this demonstration reinforced the gradual change in 
expert opinion in favor of ac over dc, and the Cataract Company 
finally decided to construct an ac system. 

After the ac system had been established, it turned out that the 
critics had been wrong in their prediction about the variation of 
demand for electricity throughout the day. Electricity was to have 
many uses besides lighting. In the 1890's, electric motors were 
already being used for street railway cars, sewing machines and 
elevators. Because of these diverse uses, the demand for electricity 
was spread out more evenly during each 24-hour period. In the 
particular case of the Niagara Falls power plant, the source of 
energy — the flow of water down the Niagara River — made it possible 
to produce energy continuously without much extra cost. (The 
boiler for a steam turbine would either have to be kept supplied 
with fuel during the night, or shut down and started up again in 
the morning.) Since hydroelectric power was available at night at 
low cost, new uses for it became possible. The Niagara Falls plant 
attracted electric furnace industries, continually producing such 
things as aluminum, abrasives, silicon and graphite. Previously 
the electrochemical processes involved in these industries had been 
too expensive for large-scale use, but cheap power now made them 
practical. These new industries in turn provided the constant 
demand for power which was to make the Niagara project even 
more profitable than had originally been expected. 

The first transmission of power to Buffalo took place in 
November 1896. By 1899, there were eight 5,000-horsepower 
units in operation at Niagara, and the stockholders of the Cataract 
Construction Company had earned a profit of better than 50% on 



SG 15.19 



94 



Faraday and the Electrical Age 




Wilson Dam {Tennessee Valley Au- 
thority), Alabanna 



r\_ 



dto 



y=M 



The general principle of hydro- 
electric power generation is shown in 
this sketch: water flowing from a 
higher to lower level turns turbine 
blades attached to a generator shaft. 
The details of construction vary widely. 




Niagara Power Plant 

their investment. By this time the electrochemical industries, 
which had not figured in the original plans at all, were using more 
power than lighting and motors together. 

As a postscript to the story- of ac versus dc. it should be 
mentioned that dc is now coming back into favor for long-distance 
transmission of electric power at very high voltages. The reasons 
for this turnabout are explained in an article, "The Future of Direct 
Current Power Transmission," reprinted in Reader 4. 

Q14 Give one reason why it is more economical to transmit 
electric power at high voltage and low current than at low voltage 
and high current. 

Q15 Why won't transformers operate if steady dc is furnished 
for the primary coil? 



15.8 Electricity and society 

Many times during the last hundred years, enthusiastic 
promoters have predicted that a marvelous future is in store for 
us all. We need only stand back and watch the application of 
electricity to all phases of life. First, the backbreaking physical 



Section 15.8 95 

labor that has been the lot of 99% of the human race throughout 
the ages (and still is for most of mankind today) will be handed 
over to machinery run by electricity; the average citizen will have 
nothing to do except supervise machinery for a few hours a day, 
and then go home to enjoy his leisure. Moreover, the old saying 
that "a woman's work is never done" will be forgotten, since 
electric machines will do all the cleaning, laundering and ironing, 
preparation of food and washing of dishes, leaving the woman free 
to do a greater variety of things than the chores of the housewife. 

A second social purpose of electrical technology was conceived 
by President Franklin D. Roosevelt and others who believed that 
country life is in some sense more natural and healthy than city 
life. In the nineteenth century, largely through the steam engine, 
a source of power came into use that could take over most work 
done by humans and animals — but only at the price of concentrating 
people in the cities, close to the power generating plant. Now that 
electrical transmission of power at a distance was possible, people 
could go back to the countryside without sacrificing the comforts 
of city life. Heating, lighting and refrigeration by electricity would 
make life easier and more sanitary in previously difficult climates. 
One of the major achievements of Roosevelt's administration in the 
1930's was the rural electrification program, which provided loans 
for rural cooperatives to install their own electrical generating and 
distribution systems in areas where the private power companies 
had previously found it unprofitable to operate. Federal power 
projects such as the Tennessee Valley Authority also assisted in the 
campaign to make electricity available to everyone. By making 
country life a bit more luxurious and reducing the physical labor 
involved in farming, electrification should have helped to reverse 
the migration of people from rural to urban areas. 

A third effect of electricity might be to help unite a large SG 15.20 

country into a single social unit by providing rapid transportation, 
and even more rapid communication between the different parts. 
Human society evolves much as do the biological organisms: all 
parts develop in step and increase their interdependence. It follows 
that telephone communications and modern civilization had to 
develop together. The telephone would be most valuable in a 
complicated cosmopolitan society and. as is now recognized, a 

sophisticated society cannot operate without a communication See "The Electronic Revolution 

system something like the telephone. Reader 4. 

Having taken care of such problems for a large part of the 
population — getting work done, finding out what's going on and 
so being able in principle to respond in time to do something about 
it, leading a healthier and more comfortable life through the use 
of refrigeration and air conditioning, man now comes face to face 
with a new problem, or rather, a problem that was encountered 
before by only a tiny fraction of the world's population. Thanks to 
advances in science and related technology, many people no longer 
have to spend almost all of their time working for the bare 
necessities of life. Now, what is it that we really want to do? 
Whatever it might be. electricity, it would seem, might help us do it 




Commercial Distribution of Electric Power 

The commercial distribution of ac electric power requires 
elaborate transmission facilities. Generator output voltages 
of about 10" volts are stepped up to about 10^ volts for 
transmission, stepped down to about 10" volts for local 
distribution, and further stepped down to about 10- volts 
by neighborhood power-pole transformers. Within the home. 
It may be stepped down further (often to 6 volts for doorbells 
and electric trains) and stepped up by transformers in radio 
and TV sets for operating high-voltage tubes. 






n 




r 



The interdependence of our modern 
system of electrical power distribution 
was dramatically demonstrated at about 
5 p.m. on November 9, 1965, when a 
faulty electrical relay in Canada caused 
a power failure and total blackout 
throughout most of the northeastern 
part of the United States. 



5'--"" -.?• 



^?r::"!5««»! 



Major electric transmission lines in the 
United States. In many cases several 
lines are represented by a single line on 
the map. Not shown are the small- 
capacity lines serving widely scattered 
populations in the mountainous and 
desert areas. In the densely populated 
areas, only the high-voltage lines 
are shown. 







:5ft'« •.. '"^'^i'! 







98 Faraday and the Electrical Age 

better. With electric lighting, we can read books at night, or attend 
meetings, plays, concerts or games in large public buildings. None 
of these things were impossible before electrical illumination was 
developed, but candles and gas lamps were messy, hard on the 
eyes, and (when used on a large scale) expensive and hazardous. 
With the telegraph, telephone, radio and television we can 
quickly learn the news of events throughout the world, benefit 
See the article on High Fidelity" from exchanging facts and opinions with other people and to some 

in Rpader 4 degree share the cultural treasures of the world. 

A less optimistic opinion. Wonderful as all this seems, a variety 
of skeptics take a much dimmer view of the "progress" cited above. 
One might argue, for example, that by exploiting the resources of 
fossH fuel (coal, oil and gas) to do work, industries in the more 
advanced countries have used up in only 200 years most of the 
reserves of chemical energy that have been accumulated over the 
last two hundred million years. Moreover, few of them have rarely 
done so with enough social conscience to avoid polluting the air 
with vast amounts of smoke and ash, except when forced to do so 
by outraged public opinion. Other skeptics claim that a social 
system has been created in which the virtues of "honest toil and 
pride of workmanship" have begun to be endangered by a working 
life of monotonous triviality for much of the population, and 
chronic unemployment for some of the rest. The rise in the 
standard of living and acquisition of new gadgets and luxuries by 
many of those living in the wealthier, industrial countries have 
not often been fulfilling real human and social needs, but were 
too frequently manipulated by advertising campaigns and planned 
obsolescence. Therefore they have not brought tranquility of spirit, 
but often only created a demand for more and more material 
possessions. Meanwhile, the materially less fortunate people are 
separated by a wider and wider gap from the richer. ones, and 
look on in growing envy and anger. 

As for the labor-saving devices sold to the modem housewife, 
have they really made things much easier for her? Housewives in 
upper- and middle-income families work usually just as much as 
before, for what appliances now do used to be done in such homes 
largely by servants. To be sure, the social changes that accompanied 
industrialization and electrification have also generated many new 
jobs for women (and men) with little training, and these jobs are 
more attractive than domestic service. This is on the plus side. But 
families with low incomes, if they can afford to buy one major 
electrical appliance, usually do not choose labor-saving gadgets 
but a television set — and most of what comes out of that, our 
skeptic says, still contributes little to a better life! 

The decentralization of population which electricity was 
supposed to produce has come about, but in an unexpected way. 
The upper- and middle-income inhabitants of cities have indeed 
been able to escape to the suburbs where they do enjoy all the 
convenience and pleasures of the electrical age. But they have 
left behind them urban ghettoes crowded with minority groups 
whose frustration at being deprived of the benefits of the "affluent 



Section 15.8 



99 



society" is only aggravated by scenes of suburban life presented to 
them on television. As for the farmer, modern technology has made 
large scale agriculture into a new kind of industry that has no 
place for the small landholder. 

Electrical communications and rapid transcontinental trans- 
portation have bound us into a close-knit, interdependent social 
system. But this has its disadvantages too. Thus, an electronic 
computer may be used by an employer or a state to dredge up all 
a man's past mistakes. 

Electricity: good or bad? The point of such criticisms is that 
it illustrates the other half of the total story: electricity, like any 
other area of technological improvement based on scientific 
discovery is neither good nor bad by itself. Electricity increases 
enormously the possibilities open to us, but choices still have to be 
made among them on the basis of value systems outside the 
framework of science or technology. The decisions about the large- 
scale apphcations of electricity cannot be left to the experts in 
physics or engineering, or to the public or private utilities, or to 
government agencies. They must be made by citizens who have 
taken the trouble to learn something about the physical forces that 
play such an important role in modern civilization — whether in 
the field of electrification, or the coming large-scale use of nuclear 
power, or the introduction of automation and other uses of 
computers, or whatever lies over the horizon. 



SG 15.21 



Electric power lines in New York State 




15.1 The Project Physics learning materials 
particularly appropriate for Chapter 15 include: 

Activities 

Faraday Disk Dynamo 

Generator Jump Rope 

Simple Meters and Motors 

Simple Motor-generator Demonstration 

Physics Collage 

Bicycle Generator 

Lapis Polaris. Magnes 

Reader Articles 

Systems. Feedback. Cybernetics 

The Electronic Revolution 

The Invention of the Electric Light 

High Fidehty 

The Future of Direct Power Transmission 

15.2 What sources of energy were there for 
industry- before the electrical age? How was the 
energy transported to where it was needed? 

15.3 Oersted discovered that a magnetic needle 
was affected by a current. Would you expect a 
magnetic needle to exert a force on the current? 
Why? How would you detect this force? 

15.4 In which of these cases will electromagnetic 
induction occur? 

(a) A battery is connected to a loop of wire held 
near another loop of wire. 

(b) A batter\- is disconnected from a loop of 
wire held near another loop of wire. 

(c) A magnet is moved through a loop of wire. 

(d) A loop of wire is held in a steadv magnetic 
field. 

(e) A loop of wire is moved across a magnetic 
field. 

15.5 Describe a set-up for producing induced 
currents by means of a magnetic field, and spell 
out how the set-up differs from one for producing 
a field by means of a current. 

15.6 It was stated on p. 84 that the output 
of a dc generator can be made smoother by 
using multiple windings. If each of two loops 
were connected to commutators as shown 
what would the output current of the generator 
be Uke? 



f 



^/ 





15.7 Refer to the simple ac generator shown on 
p. 82. Suppose the loop is being rotated counter- 
clockwise by some extemaUy applied mechanical 
force. Consider the segment b as it is pictured in 
the third drawing, moving down across the 
magnetic field. 



A useful rule: if your fingers 
point along 6, and your thumb 
along ^^ F* will be in the di- 
rection your palm would push. 
For positive charges use the 
right hand, and for negative 
use the left hand. 



(a) Use the hand rule to determine the direction 
of the current induced in b. 

(b) The induced current is an additional motion 
of charges, and they move also across the 
external magnetic field: thus an additional 
magnetic force acts on segment b. Use the 
hand rule to determine the direction of the 
additional force — but before doing so try to 
guess the direction of the force. 

(c) Determine the direction of the additional 
force on charges in the segment labeled a. 
which is moving upwards across the field. 

15.8 Why is a generator coil harder to rotate 
when it is connected to an appliance to which it 
pro\ides current, such as a lamp, than when it 
is disconnected from any load? 

15.9 Suppose two bar magnets, each held by one 
end at the same level but a few feet apart, are 
dropped simultaneously. One of them passes 
through a closed loop of wire. Which magnet 
reaches the ground first? Why? 

15.10 Sketch a situation in which a wire is 
perpendicular to a magnetic field, and use the 
hand rule to find the direction of the force on the 
current. Imagine the wire moves sideways in 
response to the force. This sideways motion is an 
additional motion across the field, and so each 
charge in the wire experiences an additional 



Multiple commutator segments of an 
automobile generator. 




100 



force. In what direction is the additional force on 
the charges? 

15.11 Connect a small dc motor to a battery 
through a current meter. By squeezing on the 
motor shaft, vary the speed of the motor. On the 
basis of your answer to question 15.10 can you 
explain the effect that the speed of the motor 
has on the current? 

1 5.1 2 A dozen Christmas-tree lights are connected 
in series and plugged into a 120-volt wall outlet. 




(a) If each lamp dissipated 10 watts of heat 
and light energy, what is the current in 
the circuit? 

(b) What is the resistance of each lamp? 

(c) What would happen to these lamps if they 
were connected in parallel across the 120- 
volt line? Why? 

15.13 Suppose we wanted to connect a dozen 
10-watt lamps in parallel across a 120-volt line, 
what resistance must each lamp have in this 
case? To determine the resistance, proceed by 
answering the following questions: 

(a) What current will there be in each lamp? 

(b) What is the resistance of each lamp? 




Compare the total current for this string of 10- 
watt lamps with the total current in the string of 
lamps in the previous question. 

15.14 A man who built his own boat wanted to 
equip it with running lights and an interior light 
using a connecting wire with a resistance of ^ 
ohm. But he was puzzled about whether a 6-volt 
system or a 12-volt system would have less 
heating loss in the connecting wires. Suppose 
that his interior lamp is to be a 6-watt lamp. (A 



6-watt lamp designed for use in 6-volt systems 
has a resistance of 6 ohms.) 

(a) If it were to operate at its full 6-volt, 6-watt 
rating, what current would the lamp require? 

(b) If the current calculated in (a) were the 
actual current, what power loss would there 
be in the connecting wires? 

(c) What would be the answers to (a) and (b) 
if he used a 12-volt battery and a 12 volt, 
6 watt bulb? 

(d) Because of the resistance of the connecting 
wires, the lamps described will not actually 
operate at full capacity. Recalculate parts 
(a) and (b) to determine what would be the 
actual currents, power losses, and power 
consumptions of the lamps. 

15.15 A transformer for an electric train is used 
to "step down" the voltage from 120 volts to 6 
volts. As in most transformers, the output power 
from the secondary coil is only a little less than 
the input power to the primary coil. Suppose the 
current in the primary coU were 4" amp, what 
would be the current in the secondary coU? 

15.16 For a transformer, the ratio of the 
secondary voltage to the primary voltage is the 
same as the ratio of the number of turns of wire 
on the secondary coil to the number of turns of 
wire on the primary coil. If a transformer were 
100 per cent efficient, the output power would 
equal the input power; assume such is the case, 
and derive an expression for the ratio of the 
secondary current to the primary current in terms 
of the turn ratio. 

15.17 On many transformers thicker wire (having 
lower resistance) is used for one of the coils than 
for the other. Which would you expect has the 
thicker wire, the low-voltage coil or the high- 
voltage coil? 

15.18 Comment on the advisability and possible 
methods of getting out of a car over which a 
high- voltage power line has fallen. 

15.19 What factors made Edison's recommenda- 
tion for the use of dc for the Niagara Falls 
system in error? 

15.20 Write a report comparing the earliest elec- 
tric automobiles with those being developed now. 

15.21 What were some of the major effects (both 
beneficial and detrimental) of electricity on 
society? 



101 



16.1 Introduction 103 

16.2 Maxwells formulation of the principles of electromagnetism 104 

16.3 The propagation of electromagnetic waves 107 

16.4 Hertz's experiments HI 

16.5 The electromagnetic spectrum 114 

16.6 What about the ether now? 121 



Radio telescope in Alaska, framed by Northern Lights 




CHAPTER SIXTEEN 



Electromagnetic Radiation 



16.1 Introduction 



On April 11. 1846, a distinguished physicist. Sir Charles 
Wheatstone. was scheduled to give a lecture at the Royal Institution 
in London. Michael Faraday was to introduce Wheatstone to the 
expectant audience of fashionable ladies and gentlemen. But at the 
last minute, just as Faraday and Wheatstone were about to enter 
the lecture hall, Wheatstone got stage fright, turned around and 
ran out into the street. Faraday felt obliged to give the lecture 
himself. As a result, we now have on record some of Faraday's 
speculations which, as he later admitted, he would never have 
made public had he not suddenly been forced to speak for an hour. 

Faraday, ordinarily so careful to confine his remarks to his 
experiments, used this occasion to disclose his speculations on the 
nature of light. They can best be understood if we recognize that 
Faraday, like Oersted before him. believed that all the forces of 
nature are somehow connected. Therefore electricity and mag- 
netism, for example, could not be separate things that just happen 
to exist in the same universe; they must really be different forms 
of the same basic phenomenon. This metaphysical conviction was 
parallel to that coming out of the speculations of Schelling and 
other German nature philosphers at the beginning of the nine- 
teenth century, and had inspired Oersted to search in the laboratory 
for a connection between electricity and magnetism. Eventually 
he found it, in his discovery that an electric current in a conductor 
can turn a nearby magnet. 

Faraday too, had been guided by a belief in the unity of natural 
forces. Could light also be considered another form of this basic 
"force"? Or rather, to ask the question using more modern termi- 
nology, is light a form o{ energy? If so, scientists should be able to 
demonstrate experimentally its connection with other forms of 
energy such as those that attend the phenomena of electricity and 
magnetism. Faraday did succeed in doing just this in 1845. when 
he showed that light traveling through heavy glass had its plane 
of polarization rotated by a magnetic field applied to the glass. 

103 



SG 16.1 



Nature philosophy was discussed 
in the Epilogue to Unit 2 Text, in 
Sec. 10.9, and its effect on Oersted 
in Sec. 14.11. 



104 



Electromagnetic Radiation 



SG 16.2 




Magnetic lines of force indicate the 
direction of magnetic force on a north 
magnetic pole. (The force on a south 
pole is in the opposite direction.) 




Electric lines of force indicate the di- 
rection of electric force on a positive 
test charge. (The force on a negative 
charge is in the opposite direction.) 



Having convinced himself by this experiment that there is a 
definite connection between hght and magnetism. Faraday could 
not resist going one step further in his impromptu lecture the 
following year. He suggested that perhaps light itself is a vibration 
of magnetic lines of force. If two charged or magnetized objects are 
connected by an electric or magnetic line of force, then Faraday 
reasoned, if one of them moves, a disturbance would be transmitted 
along the line of force. Furthermore, if light waves were vibrations 
of lines of force, then one does not need to imagine that space is 
filled with an elastic substance — ether, in order to explain the 
propagation of light. The lines of force could replace the conception 
of the ether, if one could show that lines of force have the elastic 
properties needed for wave transmission. 

Faraday could not make this idea more precise because he 
lacked the mathematical skill needed to prove that waves could be 
propagated along lines of electric or magnetic force. Other physicists 
in Britain and Europe who might have been able to develop a 
mathematical theory of electromagnetic waves did not understand 
Faraday's concept of lines of force, or at least did not consider them 
a good basis for a mathematical theory. It was not until ten years 
later that James Clerk Maxwell, a Scottish mathematical physicist 
who had just completed his B.A. degree at Cambridge University, 
saw the value of the idea of lines of force and started using 
mathematics to express Faraday's concepts. 

16.2 Maxwell's formulation of the principles of electromagnetism 

The work of Oersted, Ampere. Henry and Faraday had estab- 
lished two basic principles of electromagnetism: 

1. An electric current in a conductor produces magnetic lines 
of force that circle the conductor; 

2. When a conductor moves across externally set up magnetic 
lines of force, a current is induced in the conductor. 

James Clerk Maxwell, in the 1860's, developed a mathematical 
theory of electromagnetism in which he added to and generalized 
these principles so that they applied to electric and magnetic 
fields in conductors, in insulators, even in space free of matter. 

Maxwell proceeded by putting Faraday's theoi-y of electricity 
and magnetism into mathematical form. In 1855, less than two 
years after completing his undergraduate studies, Maxwell 
presented to the Cambridge Philosophical Society a long paper 
entitled, "On Faraday's Lines of Force. " Maxwell described how 
these lines are constructed: 

... if we commence at any point and draw a line so that, 
as we go along it, its direction at any point shall always 
coincide with that of the resultant force at that point, 
this curve will indicate the direction of that force for 
every point through which it passes, and might be called 
on that account a line offeree. We might in the same 
way draw other lines of force, till we had filled all 



Section 16.2 



105 



space with curves indicating by their direction that of the 
force at any assigned point. 
Maxwell stated that his paper was designed to "show how, by a 
strict application of the ideas and methods of Faraday, the 
connection of the very different orders of phenomena which he 
has discovered may be clearly placed before the mathematical 
mind." During the next ten years, Maxwell created his own models 
of electric and magnetic induction. In developing his theory. 
Maxwell first proposed a mechanical model to visualize the relations 
among the electrical and magnetic quantities observed experi- 
mentally by Faraday and others. Maxwell then expressed the 
operation of the model in a group of equations. These equations, 
giving the relations between the electric and magnetic fields, came 
to be the most useful way to represent the theory, and their power 
allowed him to feel free eventually to discard the mechanical model 
altogether. Maxwell's mathematical view is still considered by 
physicists to be the proper approach to the theory of electromagnetic 
phenomena. If you go on to take another physics course after this 
introductory one, you will find the development of Maxwell's 
mathematical model (Maxwell's equations) is one of the high 
points of the course; but it will require vector calculus. 

Maxwell's work contained an entirely new idea of far-reaching 
consequences: an electric field that is changing with time gen- 
erates a magnetic field. Not only do currents in conductors produce 
fields around them, but changing electric fields in insulators such 
as glass or air or the ether also produce magnetic fields. 

It is one thing to accept this newly stated connection between 
electric and magnetic fields; it is another task, both harder and 
more interesting, to understand the physical necessity for such a 
connection. The paragraphs below are intended to make it seem 
reasonable. 

An uncharged insulator (such as glass, wood, paper, rubber) 
contains equal amounts of negative and positive charge. In the 
normal state these charges are distributed evenly so that the net 
charge is zero in evei-y region of the material. But when the 
insulator is placed in an electric field, these charges are subjected 
to electrical forces; the positive charges are pushed in one direction, 
the negative in the opposite direction. None of the charges in an 
insulating material (in contrast to a conductor) are free to move far 
through the material; the charges can be displaced only a small 
distance before restoring forces in the insulator balance the force 
due to the electric field. If the strength of the field is increased, 
the charges will be displaced further. The changing displacement 
of charges that accompanies a changing electric field in an 
insulator constitutes a current. Maxwell called this current a 
displacement current. Maxwell assumed that this momentary 
displacement current in an insulator is just as effective in sur- 
rounding itself with a magnetic field as a conduction current of the 
same magnitude. 

In an insulator, the displacement current (the rate at which the 



See Maxwell's discussion "On the 
Induction of Electric Current.^ in 
Reader 4. 



\^± 



Lb 









When an electric field is set up in 
an insulating material, (as in the dia- 
gram at the right, above) the + and — 
charges, which are bound to one 
another by attraction, are displaced. 
This displacement constitues a cur- 
rent. (The + charges are represented 
by dots, and - charges by shaded 
circles.) 

SG 16.3 











106 



charge displacement changes) is directly proportional to the rate 
at which the electric field is changing in time. Thus the magnetic 
field that circles the displacement current can be considered a 
consequence of the time-varying electric field. Maxwell then 
assumed that this model, developed for matter, also applies to space 
free of matter (at first glance apparently an absurd idea) and 
therefore, that under all circumstances an electric field that is 
changing with time surrounds itself with a magnetic field. This 
principle was a new prediction of Maxwell's. Previously it was 
thought that the only current that produced a magnetic field was 
the current in a conductor. The additional magnetic field that 
Maxwell said would arise from a changing electric field, even in 
empty space, is so small in comparison to the magnetic field 
produced by the current in the conductors of the apparatus that 
it was not at that time possible to measure it directly. But, as we 
shall see. Maxwell predicted consequences that soon couW be tested. 

According to Maxwell's theory, therefore, the two basic 
principles of electromagnetism, as inherited from earlier scientists, 
should be expanded by adding a third: 

3. A changing electric field in space produces a magnetic 
field. The induced magnetic field vector B is a plane perpendicular 
to the changing electric field vector £. The magnitude of B depends 
on the rate at which E is changing. 

Thus, consider a pair of conducting plates connected to a source 
of current, as shown at the left. As charges are moved onto or away 
from plates through the conductors connecting them to the source, 
the strength of the electric field S in the space between the plates 
changes with time. This changing electric field produces a magnetic 
field B'as shown. The strength ofB*at a given moment varies with 
distance from the region between the plates. (Of course, only a 
few of the infinitely many lines for E and B are shown.) 

An additional principle was known before Maxwell, but it 
assumed new significance in Maxwell's work because it is so 
symmetrical to statement 3 above: 

4. A changing magnetic field in space produces an electric 
field. The induced electric field vector^ is in a plane perpendicular 
to the changing magnetic field vector B. The magnitude of E 
depends on the rate at which B'is changing. Consider the changing 
magnetic field produced by, say, temporarily increasing the current 



A changing electric field produces 
a magnetic field 

When the electric field f" between a 
pair of charged plates starts to in- 
crease in intensity, a magnetic field 
^ is induced. The faster £' changes, 
the more intense &is. WhenE'momen- 
tarily has reached its maximum value, 
M has decreased to zero momentarily. 
When £' diminishes, a B field is again 
induced, in the opposite direction, 
falling to zero as ? returns to its 
original strength. 



A changing magnetic field produces 
an electric field 

When the magnetic field M between 
the poles of an electromagnet starts 
to increase, an electric field E* is in- 
duced. The faster S^ changes, the more 
intense £' is. When M momentarily has 
reached its maximum value, P has 
decreased to zero momentarily. When 
W diminishes, an £* field is again in- 
duced, in the opposite direction, 
falling to zero as ^ returns to its 
original strength. 






u > 



' ' !^' " ^" » ■ 



^ 



J 1 1 k 



Section 16.3 



107 



in an electromagnet, as shown along the right side of the opposite 
page. This changing magnetic field induces an electric field in the 
region around the magnet. If a conductor happens to be aligned in 
the direction of the induced electric field, the free charges in the 
conductor will move under its influence, producing a current in the 
direction of the induced field. This electromagnetic induction had 
been discovered experimentally by Faraday, as we noted in Sec. 15.3. 

Maxwell's ideas of the total set of relations between electric 
and magnetic fields were not at once directly testable. When the 
crucial test came, it concerned his prediction of the existence of 
waves, waves travelling as interrelating electric and magnetic fields 
— electromagnetic waves. 

Q1 What did Maxwell propose is generated when there is a 
changing electric field? 

Q2 What is a displacement current? 

Q3 What are the four principles of electromagnetism? 



16.3 The propagation of electromagnetic waves 

Suppose we create, in a certain region of space, an electric 
field that changes with time. As we have just seen, according to 
Maxwell's theory, an electric field E that fluctuates in time simul- 
taneously induces a magnetic field B that also varies with time 
(as well as with distance from the region where we created the 
changing electric field). Similarly, a magnetic field that is changing 
with time simultaneously induces an electric field that changes 
with time (as well as with distance from the region where we 
created the changing magnetic field). 

As Maxwell realized and correctly predicted, mutual induction 
of time- and space-changing electric and magnetic fields should 
allow the following unending sequence of events: a time-varying 
electric field in one region produces a time- and space-varying 
magnetic field at points near this region. But this magnetic 
field produces a time- and space-varying electric field in the 
surrounding space. And this electric field, produces time- and 
space-varying magnetic fields, in its neighborhood, and so on. Thus 
if an electromagnetic disturbance is started at one location, say by 
vibrating charges (as may be imagined to exist in a hot gas, or in 
the transmitter wire of a radio or television station), the disturbance 
can travel to distant points through the mutual generation of the 
electric and magnetic fields. The fluctuation of interlocked electric 
and magnetic fields propagate through space in the foi-m of an 
"electromagnetic wave.' a disturbance in the electric and magnetic 
field intensities in space. 

In Chapter 12 it was shown that waves occur when a distur- 
bance created in one region produces at a later time a disturbance 
in adjacent regions. Snapping one end of a rope produces, through 
the action of one part of the rope on the other, a displacement at 
points further along the rope and at a later time. Dropping a pebble 
into a pond produces a disturbance that moves away from the 



See "The Relationship of Electricity 
and Magnetism" in Reader 4. 



The electric and magnetic field 
changes occur together, much like 
the "action" and "reaction" of 
Newton's third law. 



SG 16.4, 16.5 



108 



Electromagnetic Radiation 



Electric oscillations in a vacuum-tube 
circuit are led onto a rod in a conduct- 
ing "horn" and generate in the horn a 
variation in electric and magnetic 
fields that radiates away into space. 
This drawing is an instantaneous 
"snapshot of almost plane wave- 
fronts directly in front of such a horn. 




As was stated in Chapter 12, page 
110. the speed of propagation 
depends on both the stiffness and 
density of the medium: 



speed 



density 



source as a result of the action of one part of the water on the 
neighboring parts. Time-varying electric and magnetic fields 
produce a disturbance that moves away from the source as the 
varying fields in one region create varying fields in neighbor- 
ing regions. 

What determines the speed with which the electromagnetic 
waves travel? Recall first that in the case of mechanical waves in 
a rope, or in water, the speed of propagation is determined by the 
stiffness of the material and the density of the material. Speed 
increases with increasing stiffness, but decreases with increasing 
density. This relation between wave speed, stiffness, and density 
holds for both of these mechanical wave motions, and for many 
other types of waves. Here we can only sketch out in barest outline 
how Maxwell proceeded beyond this point. Assuming that something 
analogous to this relation would hold for electromagnetic waves, 
he computed what he thought to be the "stiffness" and "density" 
of electric and magnetic fields propagating through the hypo- 
thetical ether. In finding values for these two properties of the 
electric and magnetic fields, he was guided by his mechanical 
model representing the ether in which stiffness was related to the 
electric field, and density to the magnetic field. Next, he proved 
mathematically that the ratio of these two factors, which should 
determine the wave speed, is the same for all strengths of the fields. 
Finally, Maxwell demonstrated that the speed of the waves — if 
they exist!— is a definite quantity that can be deduced from 
measurements in the laboratory. 

The necessary measurements of the factors involved had 
already been performed five years earlier by the German scientists 
Weber and Kohlrausch. Using their published values. Maxwell 



1700 



1750 



1800 



■s .3 



;:? ^ 



° 3 
& P3 




1900 



NAPOLEON I (NAPOLEON BONAPARTE) 



GEORGE WASHINGTON 



PETER THE GREAT 



QUEEN V ICTORI A 
ABRAHAM LINCOLN 



BENJAMIN FRANKLIN 



JOSEPH HENRY 



CHARLES AUGUSTIN DE COULOMB 

I 

ALESSANDRO VOLTA 



CHARLES ROBERT DARWIN 



ALBERT MICHELSON 



SIR ISAAC NEWTON 

JOSEPH PRIESTLEY 

I 

DANIEL BERNOULLI 

CHARLES FRANCOIS DUFAY 

LUIGI GALVANI 



JOHANN KARL FRIEDRICK GAUSS 
I 



LORD KELVIN (WILUAM THOMSON) 



MICHAEL FARADAY 

I , 

ANDRE MARIE AMPERE 



HANS CHRISTIAN OERSTED 

I 

THOMAS YOUNG 

I 

GEORG SIMON OHM 




LOUIS PASTEUR 



SIGMUND FREUD 



HEINRICH HERTZ 



I 



O O 

O s: 



JEAN JACQUES ROUSSEAU 

I 

IMMANUEL KANT 

I 

FRANCOIS MARIE AROUET DE VOLTAIRE 



KARL MARX 



FRIEDRICH WILHELM NIETZSCHE 



SAMUEL JOHNSON 
HENRY FIELDING 
ALEXANDER POPE 



JOHANN WOLFGANG VON GOETHE 

I 

PERCY BYSSHE SHELLEY 



EMILE ZOLA 
LEO NIKOLAEVICH TOLSTOY 



ROBERT BURNS 

SAMUEL TAYLOR COLERIDGE 

I 

WILLIAM BLAKE 



ALFRED TENNYSON 



MARK TWAIN (SAMUEL L. CLEMENS) 

GEORGE BERNARD SHAW 



^ WILLIAM HOGARTH 

< 



THOMAS GAINSBOROUGH 



FRANCISCO GOYA 



EDGAR DEGAS 

I _ 
CLAUDE MONET 

VINCENT VAN GOGH 



JOSEPH MALLORD WILLIAM TURNER 



JOHANN SEBASTIAN BACH 

'^ GEORGE FREDERICK HANDEL 

I I 

ANTONIO VIVALDI 



WOLFGANG AMADEUS MOZART 



FRANZ PETER SCHUBERT 



JOHANNES BRAHMS 



LUDWIG VON BEETHOVEN 



PETER ILYICH TCHAIKOVSKY 



RICHARD WAGNER 



110 



Electromagnetic Radiation 



With better measurements we now 
know that both Maxwell's predicted 
speed and Fizeau's measured speed 
should have come to just under 
3 > 10' m/sec. 



Maxwell had shown that In an 
electromagnetic disturbance E and 
8 should be perpendicular to each 
other and to the direction of 
propagation of the wave. Hence, in 
the terminology of Chapter 12, 
electromagnetic waves are 
transverse. And as we noted in 
Chapter 13, it was long known that 
light waves are transverse. 



For a general survey of the develop- 
ment of physical ideas leading up to 
Maxwell's theory, see the article by 
Einstein and Infeld, 'The Electro- 
magnetic Field ■ in Reader 4. 

See also James Clerk Maxwell. 
Part 11 and "Maxwell's Letters: 
a Collection " in Reader 4. 



calculated that the speed of the supposed electromagnetic waves 
should be about 311.000.000 meters per second. He was immediately 
struck by the fact that this large number was very close to a 
measured speed already well known in physics. In 1849 Fizeau had 
measured the speed of light, and had obtained a value of about 
315.000.000 meters per second. The close similaiity could have 
been a chance occurrence. But Maxwell believed that there must 
be a deep underlying reason for these two numbers being so 
nearly the same. The critical significance for physics seemed 
obvious to him and. making an enormous, ingenious leap of the 
imagination, he wrote: 

The velocity of the transverse undulations in our hypo- 
thetical medium, calculated from the electromagnetic 
experiments of MM. Kohlrausch and Weber, agrees so 
exactly with the velocity of light calculated from the 
optical experiments of M. Fizeau, that we can scarcely 
avoid the inference that light consists in the transverse 
undulations of the same medium which is the cause of 
electric and magnetic phenomena. 

Here then was an explanation of light waves, and at the same time 
joining of the previously separate sciences of electricity, magnetism, 
and optics. Realizing the great significance of his discovery. 
Maxwell turned his efforts to making the theory mathematically 
elegant and freeing it from his admittedly artificial model. 

Maxwell's synthesis of electromagnetism and optics, after it 
had been experimentally confirmed (see Sec. 16.4), was seen as a 
great event in physics. In fact, physics had known no greater time 
since the 1680's when Newton was writing his monumental work 
on mechanics. Although Maxwell's electromagnetic theory grew up 
in Maxwells mind in a Newtonian, mechanical framework, it leapt 
out of that framework and became another great general physical 
theory, a theory independent of its mechanical origins. Like 
Newtonian mechanics. Maxwell's electromagnetic field theory was 
spectacularly successful. We will see something of that success in 
the next few sections. The success went in two different directions: 
the practical and the conceptual. Practically it led to a whole host 
of modern developments, such as radio and television. On the 
conceptual level it led to a whole new way of viewing phenomena. 
The universe was not only a Newtonian machine of whirling and 
colliding parts; it included fields and energies that no machine 
could duplicate. As we will note later. Maxwell's work led eventu- 
ally to the special theory of relativity, and other physical theories 
were nourished by it also. Eventually results accumulated that 
did not fit Maxwell's theory; something more was needed. Starting 
about 1925. after a quarter century of discovery and improvisation, 
the development of quantum mechanics led to an enlarged 
synthesis that included Maxwell's electromagnetism. 

Q4 What discovery did Maxwell make upon calculating the 
speed with which electromagnetic disturbances should travel? 
Q5 What is Maxwell's svnthesis? 



Section 16.4 



111 



16.4 Hertz's experiments 

Did Maxwell's theoretical result establish without doubt that 
light actually does consist of electromagnetic waves, or even that 
electromagnetic waves exist at all? No. Most physicists remained 
skeptical for several years. The fact that the ratio of two quantities 
determined by electrical experiments came out equal to the speed 
of light certainly suggested that there is some connection between 
electricity and light; no one would seriously argue that it was only 
a coincidence. But stronger evidence was needed before the rest 
of Maxwell's theory, with its curious displacement current, could 
be accepted. 

What further evidence would be sufficient to persuade physicists 
that Maxwell's theory was correct? Maxwell showed that his theory 
could explain all the known facts about electricity, magnetism, 
and light; but so could other theories, although with less sweeping 
connection between their separate parts. To a modem physicist who 
has learned Maxwell's theory from recent textbooks, the other 
theories that were proposed in the nineteenth century would all 
seem much more complicated and artificial. But at the time. 
Maxwell's theory was not appealing to the minds of those physicists 
who were not accustomed to thinking in terms of fields. It could 
only be accepted in preference to other theories if it could be used 
to predict some new property of electromagnetism or light. 

Maxwell himself made two such predictions from his theory. 
Unfortunately, he did not live to see them verified experimentally 
in 1888; for he died at the age of 48, in 1879. Maxwell's most 
important prediction was that electromagnetic waves of many 
different frequencies could exist. All such waves would be propa- 
gated through space at the speed of light. Light itself would 
correspond to waves of only a small range of frequencies (from 
4 X 10'^ cycles/sec to 7 x io>^ cycles/sec), those that are detectable 
by the human eye. 

To test this prediction, it was necessary to invent apparatus that 
could both produce and detect electromagnetic waves, preferably 
those of frequencies other than light frequencies. This was first 
done by the German physicist Heinrich Hertz. In 1886, Hertz 
noticed a peculiar effect produced during the sparking of an 
induction coil. As was well-known, sparks sometimes jump in the 
air gap between the terminals of an induction coil (see drawing). 
You will recall (Chapter 15) that an induction coil can be used to 
produce high voltages if there are many more turns of wire on one 
side than the other. Ordinarily, air does not conduct electricity, 
but when there is a very large potential difference between two 
wires a short distance apart, a conducting pathway may be formed 
momentarily by ionization of the air molecules in the gas and a 
short burst of electricity may pass through, attended by a visible 
spark. Each visible spark produced by an induction coil is actually 
a series of many small sparks, jumping rapidly back and forth 
(oscillating) between the terminals. Hertz found he could control the 
frequency of oscillation of the jumping spark by the size and shape 
of metal plates attached to the spark gap of the induction coil. 



B 




-c^ 



c^ 



Operation of the induction coil: Start- 
ing and stopping the current in coil 
A with a vibrating switch S produces 
a rapidly changing magnetic field in 
the iron core. This rapidly changing 
field induces high voltage peaks in 
the many-turn coil B, and can cause a 
spark to jump across the air gap. 
Spark coils for use In car engines 
operate in this way. 



112 



Electromagnetic Radiation 



SG 16.6 




Heinrich Hertz (1857-1894) was born 
in Hamburg, Germany. During his 
youth he was mainly interested in 
languages and the humanities, but 
was attracted to science after his 
grandfather gave him some apparatus. 
Hertz did simple experiments in a 
small laboratory which he had fitted 
out in his home. After completing 
secondary school (and a year of mili- 
tary service) he undertook the serious 
study of mathematics and physics at 
the University of Berlin m 1878. In 
1882 he devoted himself to the study 
of electromagnetism. including the 
recent and still generally unappreci- 
ated work of Maxwell. Two years later 
he started his famous experiments on 
electromagnetic waves. During the 
course of this work, Hertz made an- 
other discovery — the photoelectric 
effect — which has had a profound in- 
fluence on modern physics. We shall 
study this effect in Chapter 18 (Unit 5). 




Spark 




itJaced Sfiark 



Now Hertz observed that when a simple piece of wire was bent 
so that there was a short gap between its two ends, and was held 
not far from an induction coil, a spark would jump across the air 
gap in the wire just when a spark jumped across the terminals 
of the induction coil. This was a curious new phenomenon. He 
reasoned that as the spark jumps back and forth across the gap of 
the induction coil it must be setting up rapidly changing electric 
and magnetic fields. According to Maxwells theory, these changes 
will propagate through space as electromagnetic waves. (The 
frequency of the waves will be the same as the frequency of 
oscillations of the sparks.) When the electromagnetic waves pass 
over the bent piece of wire, they will set up rapidly changing 
electric and magnetic fields there, too. A strong electric field 
produces a spark in the air gap, just as the transmitter field did 
between the terminals of the induction coil. Since the field is 
rapidly changing, sparks can jump back and forth between the two 
ends of the wire. This wire, therefore, serves as a detector of the 
electromagnetic waves generated by the induction coil. Hertz's 
observation of the induced spark was the first solid clue that 
electromagnetic waves do exist. 

If this interpretation is correct, and waves travel through space 
from the induction coil, then there must be a short delay between 
the appearance of the first and second spark. The spark in the 
detector cannot occur at exactly the same instant as the spark in 
the induction coil because even travelling at the speed of light it 
takes finite time interval for the wave to go from one place to the 
other. In 1888 Hertz measured the speed of these electromagnetic 
waves and found it to be, as Maxwell had predicted, the same as 
the speed of light. 

In subsequent experiments. Hertz showed that the electro- 
magnetic radiation from his induction coil has all the usual 
properties of light waves. It can be reflected at the surface of solid 
bodies, including metallic conductors, and the angle of reflection is 
equal to the angle of incidence. The electromagnetic radiation can 
be focused by concave metallic mirrors. It shows diffraction effects 
when it passes through an opening in a screen. All interference 
phenomena can be shown including standing waves. Also, electro- 
magnetic waves are refracted in passing through prisms made of 
glass, wood, plastic and other non-conducting material. All these 






M i-'^imZ 



Electromagnetic radiation of a few centimeters wavelength is generated by oscil- 
lating electric fields inside the metal horn. Experiments with this radiation show 
phenomena similar to those observed for water waves and sound waves. Below is 
a record of measurements of the intensity of a standing interference pattern of 
electromagnetic waves in front of a flat reflecting surface. The intensity was mea- 
sured by the current induced in a small detector on the end of a probe, as shown 
in the photograph. 



tittiditi 




114 



Electromagnetic Radiation 



experiments, (with more modern apparatus), can be done in your 
school laboratory. 

Hertz's experiments provided dramatic confirmation of 
Maxwell's electromagnetic theory. They showed that electromagnetic 
waves actually exist, that they travel with the speed of light, and 
that they have the familiar characteristics of light. There was now 
rapid acceptance of Maxwell's theory' by mathematical physicists, 
SG 16.7 who applied it with great success to the detailed analysis of a wide 
range of phenomena. 

Maxwell also predicted that electromagnetic wa-ves will exert a 
pressure on any surface that reflects or absorbs them. This pressure 
is very small, and experimentally it is extremely difficult to 
distinguish it from the pressure caused by air currents set up by 
heating of the surface that absorbs the waves. The technical 
difficulties involved in testing this prediction were not solved until 
1899, when Lebedev in Russia and. two years later, Nichols and 
Hull in the United States, finally confirmed the existence of 
radiation pressure. They found that this pressure has exactly the 
value predicted by Maxwell's theory. 

Thus, at the end of the nineteenth century. Maxwell's electro- 
SG 16.8 magnetic theory stood on the same level as Newton's laws of 

mechanics, as an established part of the foundations of physics. 

Q6 What predictions of Maxwell's were verified by Hertz? 

Q7 What did Hertz use as a detector of electromagnetic waves? 



16.5 The electromagnetic spectrum 



The frequency unit "cycles/sec" is 
now being given the name "hertz.' 
You will sometimes see the forms 
10' hertz. 10" cycles/sec. 10 kilo- 
cycles/sec, 1 megacycle/sec, or 
1 megahertz: all signifying the same 
frequency. Some radio stations now 
regularly announce their frequencies 
in meti?>hcrt7 nviH7\ 



Hertz's induction coil produced electromagnetic radiation with 
a wavelength of about 1 meter, about a milUon times the wave- 
length of visible light. Later experiments showed that a very wide 
and continuous variation in the wavelength (and frequency) of 
electromagnetic waves is possible; the entire possible range is 
called the electromagnetic spectrum. A range of frequencies from 
about 1 cycle/sec to 10^^ cycles/sec, corresponding to a wavelength 
range from 10" meters to 10"'^ meters, has been studied and many 
frequency regions have been put to practical use. 

Light, heat, radio waves, and x rays are names given to the 
radiations in certain regions in the electromagnetic spectrum. Each 
of these names denotes a region in which radiation is produced or 
observed in a particular way. For example, light may be perceived 
directly through its effect on the retina of the eye, but to detect 
radio waves we need electronic equipment. The named regions 
overlap; for example, some radiation is called "ultraviolet" or 
"x ray." depending on how it is produced. 

All the waves in the electromagnetic spectioim, although 
produced and detected in various ways, behave as predicted by 
Maxwell's theory. All electromagnetic waves travel through empty 
space at the same speed, the speed of light. They all cany energy; 



Section 16.5 



115 



TTkEQueKlCi/ IC «' /W' y ICT /P'' lb' 10* /»* W" ID" /i'^ w'^ lo" lo'^ lo"' ID''' A?'* /c"* Id" 10^' ,0^ 

(cyc-et/sec) '' ' ' ' • ' — • ' ^ * ' — -* ♦-- - ' --^- ' " — ' ' ^ ' ' ^- 



A^^<:.'Ml■t 



-EAve 



A.C.ft"/ee 



Ty,PM 



fApAR. 



WA\lElSlJ&TH- 



"< >e)^ ic" 10^ 10^ ID i 



10'^ 10'^ Id" /(?■*■ /«-* \D'^ 



ir>^ lo-'' Id' 



when they are absorbed, the absorber is heated. Electromagnetic 
radiation, whatever its frequency, can be emitted only by a process 
in which energy is supphed to the source of radiation. There is now 
overwhehning evidence that electromagnetic radiation originates 
from accelerated charges, as Faiaday had speculated. This charge 
acceleration may be produced in many ways: by heating materials 
to increase the vibrational energy of charged particles, by varying 
the motion of charges on an electric conductor (an antenna), or by 
causing a charged particle to change its direction. In these and 
other processes some of the energy supplied to the antenna (that 
is, the work done by the force that is applied to accelerate the 
electric charge) is "radiated" away — propagating away from the 
source in the electromagnetic wave that is generated. 

The work of Maxwell and Hertz opened up not only a new 
window to the scientific view of nature, but also prepared for a 
rapidly blooming set of new technologies, such as radio, TV, radar, 
etc. As we have done before — for example in the chapter on electric 
motors and generators, let us look at least briefly at these indirect 
consequences of a scientific advance. 

Radio. Electromagnetic waves of frequencies of 10^ to 10^ cycles/ 
sec are reflected quite well by electrically charged layers in the 
upper atmosphere. This reflection makes it possible for radio waves 
to be detected at great distances from the source. Radio signals 
have wavelengths from tens to thousands of meters. Such waves 
can easily diffract around relatively small obstacles such as trees 
or buildings, but large hills and mountains may cast "dark" shadows. 



A chart of the electromagnetic 
spectrum. 

SG 16.9 



See "The Electronic Revolution" 
Reader 4. 



SG 16.10 
SG 16.11 



-*7?*'-"-- 




-^ 



Radio waves that can transverse large distances, either directly 
or by relay, are very useful for conveying information. Communica- 
tion is accomplished by changing the signal in some way following 
an agreed code that can be deciphered by the recipient. The first 
radio communication was achieved by turning the signal on and off 
in an agreed pattern, such as Morse code. Later, sounds could be 



116 



Electromagnetic Radiation 




A "carrier" radio wave. 




AM (amplitude modulation): informa- 
tion is coded as variations in the 
amplitude of the carrier. 




FM (frequency modulation): informa- 
tion is coded as variations in the 
frequency of the carrier. 



-^Or 



coded by continuous variations in the amplitude of the broadcast 
wave (AM). Later still, the information was coded as frequency 
variations in the broadcast wave (FM). In broadcast radio and 
television, the "decoding" is done in the receiver serving the 
loudspeaker or TV picture tube, so that the output message from 
the receiver takes the same form that it had at the transmitter. 

Because signals from different stations should not be received 
at the same spot on the dial, it is necessary to restrict their 
transmission. The International Telecommunication Union (ITU) 
controls radio transmission and other means of international 
communication. Within the United States, the Federal Communica- 
tions Commission (FCC) is the government agency that regulates 
radio transmission. In order to reduce the interference of one 
stations's signal with another, the FCC assigns suitable frequencies 
to radio stations, limits their power or sometimes the power radiated 
in particular directions, and may restrict the hours of transmission. 

Television and radar. Television and FM broadcasting stations 
operate at frequencies of about 10" cycles/sec or wavelengths of 
about one meter. Waves at these frequencies are not reflected by the 
layers of electric charge in the upper atmosphere; the signals travel 
in nearly straight lines and pass into space instead of following the 
curvature of the earth. Thus, they can be used to link the earth to 
stations on the moon, for example. On the other hand, coaxial 
cables or relay stations are necessary to transmit signals between 
points on the earth separated by more than about 50 miles, even if 
there are no mountains. Signals can be transmitted from one 
distant place to another, including from one continent to another 
by relay satellites. 




Satellites are used to relay microwaves 
all over the world. The microwaves 
can carry radio or TV Information. 



SG 16.12-16.18 



> 






These signals, having wavelengths of about a meter, are not 
diffracted much around objects which have dimensions of several 
meters, such as cars, ships, or aircraft. The reflected portion of 
signals of wavelengths from one meter down to as short as one 
millimeter are used to detect aircraft, ships, and other objects. The 
interference between the direct waves and reflection of these waves 
by passing airplanes can produce a very noticeable and annoying 
movement and flicker of the television picture. If the radiated 
signal is in the form of pulses, the time from the emission of a 
pulse to the reception ol its echo measures the distance of the 
reflecting object. This technique is called RAdio Detection And 
Ranging, or RADAR. By means of the reflection of a pulsed beam, 
that is pulsed, both the direction and distance of an object can 
be measured. 



Section 16.5 



117 



Infrared radiation. Electromagnetic waves with wavelengths of 
10"' to 10"^ meters are often called microwaves. The shorter the 
wavelengths, the more difficult it becomes to constiuct circuits 
that oscillate and generate significant energy of radiation. However, 
electromagnetic waves shorter than about 10"^ meters are emitted 
copiously by the very atoms of hot bodies. This "radiant heat" is 
usually called infrared rays, because most of the energy is in the 
wavelengths slightly longer than the red end of the visible band of 
radiation. While associated mainly with heat radiation, they do 
have some properties which are the same as those of visible light. 
The shorter of the infrared waves affect specially treated photo- 
graphic film, and photographs taken with infrared radiation show 
some interesting effects. Since scattering of small particles in the 
atmosphere is ver\' much less for long wavelengths (Sec. 13.6), 
infrared rays can penetrate through smoky haze dense enough to 
block visible light. 

Visible light. The visual receptors in the human eye are sensitive 
to electromagnetic radiation with wavelengths between about 
7 X 10"' and 4 x 10"" meters. Radiation of these wavelengths is 
usually light, or more explicitly, visible Ught. The peak sensitivity 
of the eye is in the green and yellow parts of the spectrum, near 
the peak of solar radiation which reaches the earth's surface. 




A photograph made with film sensi- 
tive only to infrared radiation. 



SG 16.19 
SG 16.20 




RBIATIVE. 

SBHsmvrry 
of^vm FVE. 



e^U>HLiqur 
ArUoeH 




)ilo'^ fneiers 



Ultraviolet light. Electromagnetic waves shorter than the visible 
violet are called ultraviolet. The ultraviolet region of the spectrum 
is of just as much interest in spectrum study as the visible and 
infrared because it includes radiations that are characteristic of 
many kinds of atoms. Ultraviolet light, like visible light, can also 
cause photochemical reactions in which radiant energy is converted 
directly into chemical energy. Typical of these reactions are those 
which occur in silver bromide in the photographic process, in the 
production of ozone in the upper atmosphere, and in the production 
of a dark pigment, known as melanin, in the skin. 
X rays. This radiation (wavelengths from about 10"** meters to 10"'' 
meters) is commonly produced by the sudden deflection or stopping 
of electrons when they strike a metal target. The maximum fre- 
quency of the radiation generated is determined by the energy with 
which the electrons strike the target, and that energy is determined 
by the voltage through which they are accelerated (Sec. 14.8). So 



SG 16.21 



Electromagnetic waves generally 
are produced in the acceleration 
of charged particles. 



\}^M^P^^^}\i\l\l] 




Astronomy Across the Spectrum 

Electromagnetic radiation of different wavelengths 
brings us different kinds of information. Above are 
two views of the sun on Oct. 25, 1967; at the left is 
a photo taken in violet light; at the right is a 
computer plot of intensity of very short ultraviolet 
emission. The UV doesn't penetrate the earth's 
atmosphere; the information displayed here was 
collected by the Orbiting Solar Observatory satellite 
shown at the right. Below are three views of the sun 
on Mar. 17, 1965. At the left is a photograph in red 
light; at the right is an image formed by x rays: on 
the next page is an intensity contour map made 
from the image. The x-ray telescope was raised 



above the earth's atmosphere by an Aerobee rocket. 
Longer-wavelength radiations such as radio and 






infrared are able to penetrate interstellar dust. Radio 
telescopes come in a great variety of shapes and 
sizes. Above is shown the huge Arecibo telescope in 
Puerto Rico: it has a fixed reflector but a moveable 
detector unit. To the right are a photograph and a 
diagram of a precise steerable antenna, the Haystack 
antenna in Massachusetts. Information collected with 
this instrument at 3.7 cm wavelength led to the 
upper contour map at right. This map of radio 
brightness is of the portion of the sky around the 
center of our galaxy; the area covered is about 
that of the full moon. The infrared brightness of 
the same portion of sky is shown in the bottom 
contour map. 



120 



Electromagnetic Radiation 



X-ray photos of (left) a 
Nautilus sea shell, and 
engine. 



Chambered 
(right) a jet 




The glow in the photograph is caused 
when gamma rays emitted by radio- 
active cobalt cylinders interact with 
the surrounding pool of water. 




SG 16.22 



the maximum frequency increases with the accelerating voltage. 
The higher the frequency of the x rays, the greater is their power 
to penetrate matter; the distance of penetration also depends on the 
nature of the material being penetrated. X rays are quite readily 
absorbed by bone (which contains calcium), whereas they pass 
much more readily through lower density organic matter (such as 
flesh) containing mainly the light atoms hydrogen, carbon, and 
oxygen. This fact, combined with the ability of x rays to affect a 
photographic plate, leads to some of the medical uses of x-ray 
photography. Because x rays can damage living cells they should 
be used with great caution and only by trained technicians. Some 
kinds of diseased cells are injured more easily by x rays than aie 
healthy cells, and so a carefully controlled x-ray beam can be used 
in therapy to destroy cancer or other harmful cells. 

X rays produce interference effects when they fall on a crystal 
in which atoms and molecules are arranged in a regular pattern. 
The reflected portions of the incident beam of x rays from successive 
planes of atoms in the ci^stal structure can interfere constructively, 
and this fact can be used in either of two ways. If the spacing of 
the atoms in the crystal is known, the wavelength of the x rays can 
be calculated. Conversely, if the x-ray wavelength is known, the 
distance between crystal planes, and thus the structure of the 
crystalline substance, can be determined. Hence, rays are now 
widely used by chemists, mineralogists and biologists seeking 
information about the structure of crystals and complex molecules. 

Gamma rays. The gamma-ray region of the electromagnetic 
spectrum overlaps the x-ray region (see p. 120). Gamma radiation 
is emitted mainly by the unstable nuclei of natural or artificial 
radioactive materials. We shall be considering gamma rays further 
in Unit 6. 

Q8 Why do radio waves not cast noticeable shadows behind 
such obstacles as trees or small buildings? 

Q9 Why are relay stations often needed in transmitting 
television signals? 

Q10 How is the frequency of x rays related to their penetration 
of matter? 



Section 16.6 121 

Q11 How do the wavelengths used in RADAR compare to the 
wavelengths of visible light? 

Q12 How does the production of x rays differ from that of 
gamma rays? 



16.6 What about the ether now? 

The luminiferous ether had been postulated specifically to 
serve as a medium for the propagation of light waves. Maxwell 
found that the same ether could also be thought of as a medium to 
transmit electric and magnetic forces, but also that he could 
dispense with the concept entirely if he focused on the form of the 
theor>'. Yet. just before his death in 1879, Maxwell wrote an article 
in which he still supported the ether concept: 

Whatever difficulties we may have in forming a 
consistent idea of the constitution of the aether, there 
can be no doubt that the interplanetary and interstellar 
spaces are not empty, but are occupied by a material 
substance or body, which is certainly the largest, and 
probably the most uniform body of which we have any 
knowledge. . . . 

Maxwell was aware of the failures of earlier ether theories. Near 
the beginning of the same article he said: 

Aethers were invented for the planets to swim in, to 
constitute electric atmospheres and magnetic effluvia, to 
convey sensations from one part of our bodies to another, 
and so on. till all space had been filled three or four times 
over with aethers. It is only when we remember the 
extensive and mischievous influence on science which 
hypotheses about aethers used formerly to exercise, that 
we can appreciate the horror of aethers which sober- 
minded men had during the 18th century\ . . . 

Why. after he had succeeded in formulating his electromagnetic 
theory mathematically in a way that made it independent of any 
detailed model of the ether, did Maxwell continue to speak of the 
"great ocean of aether" filling all space? Like all men. Maxwell 
could go only so far in changing his view of the world. It was 
almost unthinkable that there could be vibrations without some- 
thing that vibrates — that there could be waves without a medium. 
Also, to many nineteenth-century physicists the idea of "action at 
a distance" seemed absurd. How could one object exert a force on 
another body far away if something did not transmit the force? One 
body is said to act on another, with the word on conveying the idea 
of contact. Thus, according to accepted ways of describing the 
world using the common language, the postulate of the ether 
seemed somehow necessary. 



<') 



A.A..,..^,......^.,''-- 

»•*•■••* " " —' 

-» •*/^.. <, / ,., „. -^ / 

<fc ~ /..._,^..„*.>/— '^^■''" 



r^ 



't*-/- 







f « /V- *-' -/« A««/«~. ../—*""< 



Xh^ 




James Clerk Maxwell (1831-1879) was born In 
Edinburgh, Scotland in the same year Faraday 
discovered electromagnetic induction. Unlike 
Faraday, Maxwell came from a well-off family, 
and was educated at the Edinburgh Academy 
and the University of Edinburgh. He showed a 
lively interest in how things happened when 
he was scarcely three years old. As a child he 
constantly asked, "What's the go of that?" His 
intuition developed from mechanisms, from a 
toy top to a commercial steam engine, until 
he had satisfied his curiosity about how they 
worked. On the abstract side, his formal 
studies, begun at the Academy in Edinburgh 
and continued through his work as an under- 
graduate at Cambridge, gave Maxwell 
experience in using mathematics to develop 
useful parallels among apparently unrelated 
occurences. While Maxwell was still at the 
Edinburgh Academy, he wrote a paper on 
"Oval Curves," some pages from which are 
reproduced on this page. A summary of this 
paper was published in the proceedings of the 
Poyal Society of Edinburgh when he was only 
fourteen years old. By the time he was 
seventeen he had published three papers on 
the results of his original research. In the 
1870's he organized the Cavendish Laboratory 
at Cambridge University, which became a 
world center for physics research for the 
next several decades. 

He was one of the main contributors to 
the kinetic theory of gases, to two other 
important branches of physics, statistical 
mechanics and thermodynamics, and also the 
theory of color vision. His greatest achieve- 
ment was his electromagnetic theory. Maxwell 
is generally regarded as the most profound 
and productive physicist between the time of 
Isaac Newton and that of Albert Einstein. 




Section 16.6 



123 



Yet twenty-five years after Maxwell's death the ether concept 
had lost much of its support, and within another decade, it was 
dropped from the physicists' collection of useful concepts. In part, 
the success of Maxwell's theory itself, with its indifference to 
details of the ether's constitution, helped to undermine the general 
belief in the existence of an ether. Maxwell's equations could be 
considered to give the relations between changes of electric and 
magnetic fields in space without making any reference to the ether. 

Another difficulty with the belief in the existence of the ether 
was the failure of all attempts to detect the motion of the earth 
with respect to the ether. If light is a kind of vibration of the ether 
that pervades all space, then light should travel at a definite speed 
relative to the ether. But it seemed reasonable to assuine that the 
earth is moving through the ether as it makes its annual orbit 
around the sun. That is, the earth should be moving like a ship 
against an "ether wind" at some times and with it at other times. 
Under these conditions the apparent speed of light should be 
observed to differ, when the earth and a beam of light are moving 
in the same direction through the ether, from the speed when the 
earth and light are moving in opposite directions through the ether. 

When the time for light to make a round trip with and against 
the ether wind is computed, and is compared with the time 
calculated for a round trip in the absence of an ether wind, the 
expected time difference is found to be very small: only 10"'* 
seconds for a round trip of 30 meters. Although this is too short 
a time difference to measure directly, it is of the same order as the 
time for one vibration of visible light. It was therefore thought it 
might be detected from observations of an appropriately produced 
interference pattern. In 1887 the American scientists Albert 
Michelson and Edward Morley used a device that was so sensitive 
that it should have been able to detect an effect only one percent 
as great as that expected on the basis of the other theory. Neither 
this experiment nor the many similar experiments done since then 
have revealed an ether wind. 

In an attempt to preserve the idea of an ether, supporters of the 
ether concept offered various explanations for this unexpected 
result. For example, they suggested that objects moving at high 
speeds relative to the ether might change their size in just such a 
way as to make this relative speed undetectable. The artificiality of 
such attempts to rescue the ether concept was felt even by those 
who made these proposals. The conclusive development that led 
scientists to forego the ether concept was not a specific experiment, 
but a brilliant proposal, by a young man of 26 years, that a new 
and deep union of mechanics and electromagnetism could be 
achieved without the ether model. The man was Albert Einstein. 
A few brief remarks must suffice here to provide a setting for your 
further study of relativity at a later time. 

In 1905, Einstein showed that the equations of electx'o- 
magnetism can be written to fit the same principle of relativity 
that holds for mechanics. As you recall from Sec. 4.4, the Galilean 



SG 16.23 



An analogous effect is observed 
with sound waves; they go faster 
with respect to the ground when 
traveling in the same direction as 
the wind than they do when travel- 
ing against the wind. 



Michelson first tried the experiment 
in 1881, stimulated by a '-♦<"- "* 
Maxwell's published ju 

MaYuu<iir= Heath 



More on relativity thee 

in Chapter 20 and in Reader 



124 



Electromagnetic Radiation 




Einstein in 1912. 

See Einstein s essay On the Method 
of Theoretical Physics in Reader 4. 



Some of the other important con- 
sequences of Einstein's theory of 
relativity will be discussed In 
Unit 5. 



SG 16.24-16.28 



principle of relativity states that the same laws of mechanics apply 
in each of two frames of reference which have a constant velocity 
relative to each other. Thus it is impossible, according to this 
principle, to tell by any kind of mechanical experiment whether 
or not one's laboratory' (reference frame) is at rest or is moving 
with constant velocity. The principle is illustrated by the common 
experience that within a ship. car. plane or train moving at a 
constant speed in a straight line, the observer finds that objects 
move, or remain at rest, or fall or respond to applied force in just 
the same way they do when these conveyances are at rest. Galileo, 
a convinced Copemican. used this principle to argue that the 
motion of objects with respect to the earth (for example the fall of 
a stone along the side of a tower) gives no indication whether the 
earth is fixed and the sun in motion, or the sun fixed and the 
earth moving. 

Einstein conjectured that this principle of relativity applied not 
only to mechanics but to all of physics, including electromagnetism. 
A main reason for this assumption appears to have been his 
feeling that nature cannot be so lopsided that a principle of 
relativity should apply only to part o/ physics. Then he added a 
second basic conjecture, the statement that the speed of any light 
beam moving through free space is the same for all observers, 
even when they are moving relative to each other or relative to the 
hght sources. This bold intuition resolved the question of why the 
motion of observers with respect to the ether did not show up in 
experiments on the speed of light. In fact. Einstein simply rejected 
the ether and all other attempts to provide a "preferred frame of 
reference" for light propagation. The price of making these 
assumptions was. Einstein showed, the necessity of revising some 
common-sense notions of space and time. Einstein showed that 
Maxwells equations are fully consistent with extending the principle 
of relati\dty to all physics. This was yet another great synthesis of 
previously separate ideas analogous to those of Copernicus. 
Newton, and Maxwell. 

What then, was the role played by the elaborate theories of 
ether that were at the base of much of nineteenth-centun, physics? 
It would certainly be unjust to say that the ether conception was 
useless, since it guided the work of Maxwell and others, and also 
had useful by-products in contributing to an understanding of the 
elastic properties of matter. We should consider the early mechanical 
models used for light and electricity as the scaffolding which is 
needed to erect a building: once the building is completed, providing 
the construction is sound, the scaffolding can be torn down and 
taken away. 

Indeed the whole conception of explanation by means of 
mechanism, while intuitively appealing, has been found insufficient 
in modem physics and has been largely abandoned. Important 
developments in twentieth-centun physics that have demonstrated 
the inadequacy of mechanical explanation will be discussed in 
Units 5 and 6. 



Section 16.6 



125 



Q13 Why did Maxwell (and others) cling to the concept of 
an ether? 

Q14 Whose argument finally showed that the ether was an 
unnecessary hypothesis? 



In this chapter you have read about how mechanical models of light and 
electromagnetism faded away, leaving a model-less, mathematical, and 
therefore abstract field theory. The situation might be likened to that of 
the Cheshire Cat, in a story written by the Reverend Charles Dodgson, a 
mathematics teacher at Oxford, in 1862. Some excerpts are reproduced below. 




I Wish \ou wouldn t keep 
appearing and vanishing so 
suddenly," replied Alice, "you 
make one quite giddy." "All 
right," said the Cat; and this 
time it vanished quite slowly 
beginning with the end of the 
tail and ending with the grin, 
which remained some time 
after the rest of it had gone. 
"Well! I've often seen a cat 
without a grin," thought Alice, 
"but a grin without a cat! It's 
the most curious thing I ever 
saw in my life!" 

[Alice's Adventures in 
Wonderland, Chapter VI] 








126 Light and Electromagnetism 

EPILOGUE In this unit we have followed a complex but coherent 
story — how light and electromagnetism became comprehensible, first 
separately and then together. The particle model of light accounted for 
the behavior of light by showing that moving particles, on experiencing 
strong forces at a boundary, can be thought of as bouncing back or 
swerving in just the direction that light is observed to be reflected and 
refracted. The wave model also accounted well for these and other 
effects by treating light as transverse waves in a continuous medium. 
These rival models of light provided a substantial mechanical analogy 
for light viewed either as corpuscles or waves. 

The approach through mechanical analogy worked, up to a point, 
in explaining electricity and magnetism. Both Faraday and Maxwell 
made use of mechanical models for electric and magnetic lines of force. 
Maxwell used these models as guides to the development of a mathe- 
matical theory of electromagnetism that, when completed, went well 
beyond the models-and that also explained light as an electromagnetic 
wave phenomenon. 

The electric and magnetic fields of Maxwell's theory cannot be 
made to correspond to the parts of any mechanical model. Is there, 
then, any way we can picture in our minds what a field "looks like?" 
Here is the response of the Nobel Prize-winning American physicist 
Richard Feynman to this question: 

I have asked you to imagine these electric and magnetic 
fields. What do you do? Do you know how? How do I imagine 
the electric and magnetic field? What do I actually see? 
What are the demands of scientific imagination? Is it any 
different from trying to imagine that the room is full of 
invisible angels? No, it is not like imagining invisible angels. 
It requires a much higher degree of imagination to under- 
stand the electromagnetic field than to understand invisible 
angels. Why? Because to make invisible angels understand- 
able, all I have to do is to alter their properties a little bit-\ 
make them slightly visible, and then I can see the shapes of 
their wings and bodies, and halos. Once I succeed in 
imagining a visible angel, the abstraction required — which is 
to take almost invisible angels and imagine them completely 
visible — is relatively easy. So you say, "Professor, please give 
me an approximate description of the electromagnetic 
waves, even though it may be slightly inaccurate, so that I 
too can see them as well as I can see almost invisible angels. 
Then I will modify the picture to the necessary abstraction." 

I'm sorry that I can't do that for you. I don't know how. 
I have no picture of this electromagnetic field that is in any 
sense accurate. I have known about the electromagnetic 
field a long time- 1 was in the same position 25 years ago 
that you are now, and I have had 25 years of experience 
thinking about these wiggling waves. When I start describing 
the magnetic field moving through space, I speak of the E- 
and e-fields and wave my arms and you may imagine that 
I can see them. I'll tell you what I can see. I see some kind of 
vague shadowy wiggling lines — here and there is an E and B 



Epilogue 



127 



written on tinem someliow, and perhaps some of the lines 
have arrows on them -an arrow here or there which 
disappears when I look too closely at it. When I talk about 
the fields swishing through space, I have a terrible confusion 
between the symbols I use to describe the objects and the 
objects themselves. I cannot really make a picture that is 
even nearly like the true waves. So if you have some 
difficulty in making such a picture, you should not be 
worried that your difficulty is unusual. 

[A more extended excerpt of this discussion may be found in Reader 4.] 

We can summarize the general progression represented by the 
development of mechanics and electromagnetism by saying that 
physical theories have become increasingly abstract and mathematical. 
Newton banished the celestial machinery of early theories by sub- 
stituting a mathematical theory using the laws of motion and the 
inverse-square law. Maxwell developed a mathematical theory of 
electromagnetism that, as Einstein showed, did not require any 
all-pervading material medium. We are seeing here a growing but quite 
natural disparity between common-sense ideas that develop from direct 
human experiences and the subtle mathematical abstractions developed 
to deal with effects that we cannot sense directly. 

Yet these highly abstract theories do ultimately have to make sense 
when couched in ordinary language, and they do tell us about the 
things we can see and touch and feel. They use abstract language, 
but have concrete tests and by-products. They have made it possible 
to devise the equipment that guides space probes to other planets and 
to design and operate the instruments that enable us to communicate 
with these probes. Not only are these theories at the base of all practical 
developments in electronics and optics, but they now also contribute 
to our understanding of vision and the nervous system. 

Maxwell's electromagnetic theory and the interpretation given to 
electromagnetism and mechanics by Einstein in the special theory of 
relativity produced a profound change in the basic philosophical 
viewpoint of the Newtonian cosmology. (In this sense, Unit 4 marks a 
kind of watershed between the "old" and "new" ways of doing physics.) 
While it is too early to hope for a comprehensive statement of these 
changes, some aspects of a new cosmology can already be detected. 
For this purpose, we must now give further attention to the behavior 
of matter, and to the atomic theories developed to account for 
this behavior. 







16.1 The Project Physics learning materials 
particularly appropriate for Chapter 16 
include: 

Experiment 

Electromagnetic radiation 
Activities 

Microwave Transmission System 

Science and the Artist- the Stor\ Behind a 
New Science Stamp 

Bell Telephone Science Kits 

Good Reading 
Reader Articles 

James Clerk Maxwell. Part II 

On the Induction of Electric Current 

The Relationship of Electricity and Magnetism 

The Electromagnetic Field 
Film Loop 

Standing Electromagnetic Waves 
Transparency 

The Electromagnetic Spectrum 

16.2 What inspired Oersted to look for a connec- 
tion between electricity and magnetism? 

16.3 A current in a conductor can be caused by 

a steady electric field. Can a displacement current 
in an insulator be similarly caused? Explain your 
answer briefly. 

16.4 What causes an electromagnetic wave to be 
initiated? to be propagated? 

16.5 What is the "disturbance" that travels in 
each of the following waves: 

(a) w ater w aves 

(b) sound waves 

(c) electromagnetic waves 

16.6 In Hertz's detector, it is the electric field 
strength in the neighborhood of the wire that 
makes the sparks jump. How could Hertz show- 
that the waves from the induction coil spark gap 
were polarized? 

16.7 What evidence did Hertz obtain that his 
induction-coil-generated waves have many 
properties similar to visible light waves? 

16.8 Give several factors that contributed to 
the twenty-five year delay in the general 
acceptance by scientists of Maxwell's electro- 
magnetic wave theory-. 

16.9 What evidence is there for believing that 
electromagnetic waves carry energy? Since the 
energy travels in the direction of wave 
propagation, how^ does this suggest why the early 
particle theory of light had some success? 

16.10 VVhat is the wavelength of an electromag- 
netic wave generated by the 60 cycles sec 
alternating current in power lines? 

16.11 How short are ■short-wave" radio waves? 
(Look at the frequencies indicated on the dial 

of a short-wave radio.) 



16.12 Electric discharges in sparks, neon signs, 
lighting, and some atmospheric disturbances 
produce radio waves. The result is "static " or 
noise in AM radio receivers. Give other likely 
sources of such static. 

16.13 Why is there federal control on the 
broadcast power and direction of radio and T\' 
stations, but no comparable controls on the 
distribution of newspapers and magazines? 

16.14 If there are extraterrestial beings of 
advanced civilizations, what method for gathering 
information about earth-people would be available 
to them? 

16.15 Why can radio waves be detected at 
greater distances than the waves used for 
television and FM broadcasting? 

16.16 Some relay satellites have a 24-hour orbit, 
to stay above the same point as the earth turns 
below it. What would the radius and location of 
the orbit of such a "synchronous" orbit be? (Refer 
to Unit 2 for whatever principles or constants 
you need.) 

16.17 Explain why airplanes passing overhead 
cause "flutter" of a TV picture. 

16.18 How much time would elapse between the 
sending of a radar signal to the moon and the 
return of the echo? 

16.19 Refer to the black-and-white photograph 
on p. 117 that was taken using film sensitive 
only to the infra-red. How do you account for the 
appearance of the trees, clouds, and sky? 

16.20 What do you think is the reason for the 
eye to be sensitive to the range of light w ave- 
lengths that it is? 

16.21 A sensitive thermometer placed in different 
parts of the visible light spectrum formed by a 
quartz prism will show a rise in temperature. 
This shows that all colors of light produce heat 
when absorbed. But the thermometer also shows 
an increase in temperature when its bulb is 
placed in either of the two dark regions to either 
side of the end of the visible spectrum. Why 

is this? 

16.22 For each part of the electromagnetic 
spectrum discussed in Sec. 16.5. list the ways 
in which you have been aff"ected by it. Give 
examples of things you have done with radiation 
in that frequency range, or of eflects it has 

had on you. 

16.23 What is the principal reason for the loss 
of support for the ether concept? 

16.24 At many points in the histor>" of science 
the "naturar" or "intuitively" obvious way of 
looking at things has changed radically Our 



128 



attitudes toward action-at-a-distance are a case 
in point. What are some other examples? 

16.25 Can intuition be educated? that is, can 
our feelings about what the fundamental aspects 
of reality are be changed? Use attitudes taken 
toward action-at-a distance of the ether as one 
example, and give others. 

16.26 Explain the analogy of the cat-less grin 
given at the end of Chapter 16. 

16.27 Write a brief essay on any two of the five 
pictures on pages 126 and 127, explaining in 
some detail what principles of physics they 



illustrate. (Select first the main principle at work 
in each of the situations shown here. Also you 
need not limit yourself to the principles discussed 
in this unit.) 

16.28 In a couple of pages, summarize how this 
unit built up the story (and physical details) of 
the theory of light — from the particle model of 
light, to the model of light as a material wave in 
a material ether, to the joining of the initially 
separate disciplines of electricity and magnetism, 
first with each other and then with the theory of 
light in the general electromagnetic theory of 
Maxwell. 



When signals are led to several antennas, the interference among their radiated 
waves can result in the broadcast power being restricted to certain directions. This 
elaborate antenna array is a U.S. Navy installation at Cutler, Maine. 




129 



Picture Credits, Text Section (cont.) 

P. 120 (top left) Courtesy of General Electric 
Company, X-ray Department; (top right) Eastman 
Kodak Company, Rochester, New York; (bottom 
left) Brookhaven National Laboratory. 

P. 122 (manuscript) Royal Society of Edin- 
burgh, Scotland; (portrait) Trinity College Library, 
Cambridge, England. 

P. 125 John Tenniel drawings. 

P. 129 TEMCO Electronics Photo-lab, Garland, 
Texas. 

All photographs not credited above were made 
by the stafF of Harvard Project Physics. 



Picture Credits. Handbook Section 

Cover; (upper left) Cartoon by Charles Gary 
Solin and reproduced by his permission only; 
(diffraction pattern) Cagner, Francon and Thrierr, 
Atlas of Optical Phenomena, 1962, Springer- 
verlag OHG, Berlin. 

P. 141 (cartoon) By permission of Johnny Hart 
and Field Enterprises. Inc. 



Pp. 143, 146, 154, 168, 177 (cartoons) By 
Charles Gary Solin and reproduced by his per- 
mission only. 

P. 168 Collage, "Physics" by Bob Lillich. 

P. 169 Burndy Library. 

All photographs and notes used with film loops 
courtesy of the National Film Board of Canada. 

Photographs of laboratory equipment and of 
students using laboratory equipment were sup- 
plied with the cooperation of the Project Physics 
staff and Damon Corporation. 



Acknowledgments. Handbook Section 

Pp. 159, 160 Smedile, S. Raymond, More 
Perpetual Motion Machines, Science Publications 
of Boston, 1962. 

Pp. 175, 176 "Science and the Artist," 
Chemistry, January 1964, pp. 22-23. 

P. 163 I. F. Stacy, The Encyclopedia of 
Electronics (Charles Susskind, Ed.), Reinhold 
Publishing Corp., N.Y., Fig. 1, p. 246. 




The Project Physics Course 



Handbook 



Light and Electromagnetism 







staff and Consultants 



Robert Gardner, Harvard University 
Fred Geis, Jr., Harvard University 
Nicholas J. Georgis, Staples High School, 

Westport, Conn. 
H. Richard Gerfin, Somers Middle School, 

Somers, N.Y. 
Owen Gingerich, Smithsonian Astrophysical 

Observatory, Cambridge, Mass. 

Stanley Goldberg, Antioch College, Yellow Springs, 

Ohio 
Leon Goutevenier, Paul D. Schreiber High School, 

Port Washington, N.Y. 
Albert Gregory, Harvard University 
Julie A. Goetze, Weeks Jr. High School, Newton, 

Mass. 
Robert D. Haas, Clairemont High School, San 

Diego, Calif. 
Walter G. Hagenbuch, Plymouth-Whitemarsh 
Senior High School, Plymouth Meeting, Pa. 
John Harris, National Physical Laboratory of 

Israel, Jerusalem 
Jay Hauben, Harvard University 
Peter Heller, Brandeis University, Waltham, Mass. 
Robert K. Henrich, Kennewick High School, 

Washington 
Ervin H. Hoffart, Raytheon Education Co., Boston 
Banesh Hoffmann, Queens College, Flushing, N.Y. 
Elisha R. Huggins, Dartmouth College, Hanover, 

N.H. 
Lloyd Ingraham, Grant High School, Portland, 

Ore. 
John Jared, John Reimie High School, Pointe 

Claire, Quebec 
Harald Jensen, Lake Forest College, 111. 
John C. Johnson, Worcester Polytechnic Institute, 

Mass. 
Kenneth J. Jones, Harvard University 
LeRoy Kallemeyn, Benson High School, Omaha, 

Neb. 
Irving Kaplan, Massachusetts Institute of 

Technology, Cambridge 
Benjamin Karp, South Philadelphia High School, 

Pa. 
Robert Katz, Kansas State University, Manhattan, 

Kans. 
Harry H. Kemp, Logan High School, Utah 
Ashok Khosla, Harvard University 
John Kemeny National Film Board of Canada, 

Montreal 
Merritt E. Kimball, Capuchino High School, San 

Bruno, Calif. 
Walter D. Knight, University of California, 

Berkeley 
Donald Kreuter, Brooklyn Technical High School, 

NY. 
Karol A. Kunysz, Laguna Beach High School, 

Calif. 
Douglas M. Lapp, Harvard University 
Leo Lavatelli, University of Illinois, Urbana 



132 



Joan Laws, American Academy of Arts and 

Sciences, Boston 
Alfred Leitner, Michigan State University, East 

Lansing 
Robert B. LiUich, Solon High School, Ohio 
James Lindblad, LoweU High School, Whittier, 

Calif. 
Noel C. Little, Bowdoin College, Brunswick, Me. 
Arthur L. Loeb, Ledgemont Laboratory, Lexington, 

Mass. 
Richard T. Mara, Gettysburg College, Pa. 
Robert H. Maybury, UNESCO, Paris 
John McClain, University of Beirut, Lebanon 
E. Wesley McNair, W. Charlotte High School, 

Charlotte, N.C. 
William K. Mehlbach, Wheat Ridge High School, 

Colo. 
Priya N. Mehta, Harvard University 
Glen Mervyn, West Vancouver Secondary School, 

B.C., Canada 
Franklin Miller, Jr., Kenyon College, Gambler, 

Ohio 
Jack C. Miller, Pomona College, Claremont, Calif. 
Kent D. Miller, Claremont High School, Cahf. 
James A. MinstreU, Mercer Island High School, 

Washington 
James F. Moore, Canton High School, Mass. 
Robert H. Mosteller, Princeton High School, 

Cincinnati, Ohio 
William Naison, Jamaica High School, N.Y. 
Henry Nelson, Berkeley High School, Calif. 
Joseph D. Novak, Purdue University, Lafayette, 

Ind. 
Thorir Olafsson, Menntaskolinn Ad, Laugarvatni, 

Iceland 
Jay Orear, Cornell University, Ithaca, N.Y. 
Paul O'Toole, Dorchester High School, Mass. 
Costas Papaliolios, Harvard University 
Jacques Parent, National Film Board of Canada, 

Montreal 
Father Thomas Pisors, C.S.U., Griffin High 

School, Springfield, 111. 
Eugene A. Platten, San Diego High School, Calif. 
L. Eugene Poorman, University High School, 

Bloomington, Ind. 
Gloria Poulos, Harvard University 
Herbert Priestley, Knox College, Galesburg, 111. 
Edward M. Purcell, Harvard University 
Gerald M. Rees, Ann Arbor High School, Mich. 
James M. Reid, J. W. Sexton High School, 

Lansing, Mich. 
Robert Resnick, Rensselaer Polytechnic Institute, 

Troy, N.Y. 
Paul I. Richards, Technical Operations, Inc., 

Burlington, Mass. 
John Rigden, Eastern Nazarene College, Quincy, 

Mass. 
Thomas J. Ritzinger, Rice Lake High School, Wise. 
Nickerson Rogers, The Loomis School, Windsor, Conn. 

(continued on p. 179) 



Contents 



HANDBOOK SECTION 



Chapter 13 Light 

Experiments 

32. Refraction of a Light Beam 134 

33. Young's Experiment— The Wavelength 

ofhght 136 
Activities 
Thin Film Interference 138 
Handkerchief Diffraction Grating 138 
Photographing Diffraction Patterns 138 
Poisson's Spot 139 
Photographic Activities 139 
Color 139 
Polarized Light 140 
Making an Ice Lens 141 

Chapter 14 Electric and Magnetic Fields 

Experiments 

34. Electric Forces I 142 

35. Electric Forces II— Coulomb's Law 144 

36. Forces on Currents 147 

37. Cun-ents, Magnets, and Forces 152 

38. Electron Beam Tube 155 
Activities 

Detecting Electric Fields 158 

Voltaic Pile 158 

An ll(i Battery 158 

Measuring Magnetic Field Intensity 158 

More Perpetual Motion Machines 159 

Additional Activities Using the Electron 

Beam Tube 160 
Transistor Amphiier 162 



Inside a Radio Tube 163 
An Isolated North Pole? 164 

Chapter 15 Faraday and the Electrical Age 

Activities 

Faraday Disk Dynamo 165 

Generator Jump Rope 165 

Simple Meters and Motors 166 

Simple Motor-Generator Demonstration 167 

Physics Collage 168 

Bicycle Generator 168 

Lapis Polaris, Magnes 168 

Chapter 16 Electromagnetic Radiation 

Experiment 

39. Waves and Communication 170 

A. Turntable Oscillators 170 

B. Resonant Circuits 171 

C. Elementary Properties of Microwaves 171 

D. Interference of Reflected Microwaves 172 

E. Signals and Microwaves 174 
Activities 

Microwave Transmission Systems 175 
Science and the Artist— The Story Behind 

a New Science Stamp 175 
Bell Telephone Science Kits 177 
Film Loop 

Film Loop 45 : Standing Electromagnetic 
Waves 178 



133 



Chapter 



13 



Light 



EXPERIMENT 32 

REFRACTION OF A LIGHT BEAM 

You can easily demonstrate the behavior of a 
light beam as it passes from one transparent 
material to another. All you need is a semi- 
circular plastic dish, a lens, a small light 
source, and a cardboard tube. The light source 
from the Milhkan apparatus (Unit 5) and the 
telescope tube with objective lens (Units 1 
and 2) will serve nicely. 

Making a Beam Projector 

To begin with, slide the Millikan apparatus 
light source over the end of the telescope tube 
(Fig. 13-1). When you have adjusted the bulb- 
lens distance to produce a parallel beam of 
light, the beam will form a spot of constant size 
on a sheet of paper moved toward and away 
from it by as much as two feet. 

Make a thin flat light beam by sticking two 
pieces of black tape about 1 mm apart over the 
lens end of the tube, creating a slit. Rotate the 
bulb filament until it is parallel to the slit. 



blo^tk ''■o-pe. 




Fig. 13-1 



When this beam projector is pointed 
slightly downward at a flat surface, a thin 
path of light falls across the surface. By direct- 
ing the beam into a plastic dish filled with 
water, you can observe the path of the beam 
emerging into the air. The beam direction can 
be measured precisely by placing protractors 
inside and outside the dish, or by placing the 
dish on a sheet of polar graph paper. (Fig. 13-2) 




Fig. 13-2 

Behavior of a Light Beam at the Boundary 
Between Two Media 

Direct the beam at the center of the flat side 
of the dish, keeping the slit vertical. Tilt the 
projector until you can see the path of light 
both before it reaches the dish and after it 
leaves the other side. 

To describe the behavior of the beam, you 
need a convenient way of referring to the angle 
the beam makes with the boundary. In physics, 
the system of measuring angles relative to a 
surface assigns a value of 0° to the perpendic- 
ular or straight-in direction. The angle at which 
a beam strikes a surface is called angle of 
incidence; it is the number of degrees away 
from the straight-in direction. Similarly, the 
angle at which a refracted beam leaves the 
boundary is called the angle of refraction. It 
is measured as the deviation from the straight- 
out direction. (Fig. 13-3) 




Fig. 13-3 

Note the direction of the refracted beam 
for a particular angle of incidence. Then direct 
the beam perpendicularly into the rounded side 
of the dish where the refracted beam came out. 
(Fig. 13-4) At what angle does the beam now 
come out on the flat side? Does reversing the 
path like this have the same kind of effect for 
all angles? 
Ql Can you state a general rule about the 



Experiment 32 



135 




Fig. 13-4 

passage of light beams through the medium? 
Q2 What happens to the Ught beam when it 
reaches the edge of the container along a 
radius? 

Change the angle of incidence and observe 
how the angles of the reflected and refracted 
beams change. (It may be easiest to leave the 
projector supported in one place and to rotate 
the sheet of paper on which the dish rests.) 
You will see that the angle of the reflected 
beam is always equal to the angle of the in- 
cident beam, but the angle of the refracted 
beam does not change in so simple a fashion. 

Refraction Angle and Change in Speed 

Change the angle of incidence in 5° steps from 
0° to 85°, recording the angle of the refracted 
beam for each step. As the angles in air get 
larger, the beam in the water begins to spread, 
so it becomes more difficult to measure its 
direction precisely. You can avoid this diffi- 
culty by directing the beam into the round 
side of the dish instead of into the flat side. 
This will give the same result since, as you 
have seen,\the light path is reversible. 
Q3 On the basis of your table of values, does 
the angle in air seem to increase in proportion 
to the angle in water? 

Q4 Make a plot of the angle in air against the 
angle in water. How would you describe the 
relation between the angles? 

According to both the simple wave and 
simple particle models of light, it is not the 
ratio of angles in two media that will be con- 
stant, but the ratio of the sines of the angles. 
Add two columns to your data table and, refer- 
ring to a table of the sine function, record the 
sines of the angles you observed. Then plot 
the sine of the angle in water against the sine 
of the angle in air. 

Q5 Do your results support the prediction 
made from the models? 

Q6 Write an equation that describes the rela- 
tionship between the angles. 



According to the wave model, the ratio of 
the sines of the angles in two media is the 
same as the ratio of the hght speeds in the 
two media. 

Q7 According to the wave model, what do 
your results indicate is the speed of light in 
water? 

Color Differences 

You have probably observed in this experiment 
that different colors of hght are not refracted 
by the same amount. (This effect is called dis- 
persion.) This is most noticeable when you 
direct the beam, into the round side of the dish, 
at an angle such that the refracted beam leav- 
ing the flat side lies very close to the flat side. 
The different colors of light making up the 
white beam separate quite distinctly. 
Q8 What color of hght is refracted most? 
Q9 Using the relation between sines and 
speeds, estimate the difference in the speeds 
of different colors of light in water. 

Other Phenomena 

In the course of your observations you probably 
have observed that for some angles of in- 
cidence no refracted beam appears on the 
other side of the boundary. This phenomenon 
is called total internal reflection. 
Ql When does total internal reflection occur? 
By immersing blocks of glass or plastic in 
the water, you can observe what happens to 
the beam in passing between these media and 
water. (Liquids other than water can be used, 
but be sure you don't use one that will dissolve 
the plastic dish!) If you lower a smaller trans- 
parent container upside-down into the water so 
as to trap air in it, you can observe what hap- 
pens at another water-air boundary. (Fig. 13-5) 
A round container so placed will show what 
effect an air-bubble in water has on light. 



Fig. 13-5 

Ql 1 Before trying this last suggestion, make a 
sketch of what you think will happen. If your 
prediction is wrong, explain what happened. 



136 



EXPERIMENT 33 YOUNG'S EXPERIMENT 
-THE WAVELENGTH OF LIGHT 

You have seen how ripples on a water suri'ace 
are diffracted, spreading out after having 
passed through an opening. You have also seen 
wave interference when ripples, spreading out 
from two sources, reinforce each other at some 
places and cancel out at others. 

Sound and ultrasound waves behave like 
water waves. These diffraction and inter- 
ference effects are characteristic of all wave 
motions. If light has a wave nature, must it 
not also show diffraction and interference 
effects? 

You may shake your head when you think 
about this. If light is diffracted, this must mean 
that light spreads around comers. But you 
learned in Unit 2 that "light travels in straight 
lines." How can light both spread around 
comers and move in straight lines? 

Simple Tests of Light Waves 

Have you ever noticed light spreading out after 
passing through an opening or around an ob- 
stacle? Try this simple test: Look at a narrow 
light source several meters away from you. (A 
straight-filament lamp is best, but a single 
fluorescent tube far away will do.) Hold two 
fingers in front of one eye and parallel to the 
light source. Look at the light through the gap 
between them. (Fig. 13-6) Slowly squeeze your 
fingers together to decrease the width of the 
gap. What do you see? What happens to the 
light as you deduce the gap between your 
fingers to a very narrow slit? 




Fig. 13-6 

Evidently light can spread out in passing 
through a very narrow opening between your 
fingers. For the effect to be noticeable, the 
opening must be small in comparison to the 
wavelength. In the case of light, the opening 



must be much smaller than those used in the 
ripple tank, or with sound waves. This suggests 
that light is a wave, but that it has a much 
shorter wavelength than the ripples on water, 
or sound or ultrasound in the air. 

Do light waves show interference? Your 
immediate answer might be "no." Have you 
ever seen dark areas formed by the cancella- 
tion of light waves from two sources? 

As with diffraction, to see interference 
you must arrange for the light sources to be 
small and close to each other. A dark photo- 
graphic negative with two clear lines or slits 
running across it works very well. Hold up 
this film in front of one eye with the slits paral- 
lel to a narrow light source. You should see 
evidence of interference in the light coming 
from the two shts. 

Two-slit Interference Pattern 

To examine this interference pattern of light 
in more detail, fasten the film with the double 
slit on the end of a cardboard tube, such as the 
telescope tube without the lens. Make sure that 
the end of the tube is light-tight, except for the 
two slits. (It helps to cover most of the film 
with black tape.) Stick a piece of translucent 
"frosted" tape over the end of a narrower tube 
that fits snugly inside the first one. Insert this 
end into the wider tube, as shown in Fig. 13-7. 







lelescope Tubes 



Fig. 13-7 

Set up your double tube at least 5 feet 
away from the narrow light source with the 
slits parallel to the light source. With your eye 
about a foot away from the open end of the 
tube, focus your eye on the screen. There on 
the screen is the interference pattern formed 
by light from the two slits. 
Ql Describe how the pattern changes as you 
move the screen farther away from the slits. 
Q2 Try putting different colored filters in 



Experiment 33 



137 



front of the double slits. What are the differ- 
ences between the pattern formed in blue 
light and the pattern formed in red or yellow 
hght? 

Measurement of Wavelength 

Remove the translucent tape screen from the 
inside end of the narrow tube. Insert a mag- 
nifying eyepiece and scale unit in the end 
toward your eye and look through it at the light. 
(See Fig. 13-8) What you see is a magnified 
view of the interference pattern in the plane 
of the scale. Try changing the distance be- 
tween the eyepiece and the double slits. 



'^ Slit 



Sll+S 



Scale 




i , 



Fig. 13-8 

In Experiment 3 1 , you calculated the wave- 
length of sound from the relationship 

The relationship was derived on page 120 of 
Text Chapter 12. There it was derived for 
water waves from two in-phase sources, but 
the mathematics is the same for any kind of 
wave. (Use of two closely-spaced slits gives a 
reasonably good approximation to in-phase 
sources.) 




Fig. 13-9 ^ 

Use the formula to find the wavelength of 
the light transmitted by the different colored 
filters. To do so, measure x, the distance be- 
tween neighboring dark fringes, with the mea- 
suring magnifier (Fig. 13-10). (Remember that 
the smallest divisions on the scale are 0. 1 mm. ) 
You can also use the magnifier to measure d. 
the distance between the two slits. Place the 



Fig. 13-10 ^ 

film against the scale and then hold the film 
up to the light.) In the drawing, I is the dis- 
tance from the slits to the plane of the pattern 
you measure. 

The speed of light in air is approximately 
3 X 10* meters/second. Use your measured 
values of wavelength to calculate the approxi- 
mate light frequencies for each of the colors 
you used. 

Discussion 

Q3 Why couldn't you use the method of 
"standing waves" (Experiment 31, "Sound") 
to measure the wavelength of light? 
Q4 Is there a contradiction between the 
statement, "Light consists of waves" and the 
statement, "Light travels in straight lines"? 
Q5 Can you think of a common experience in 
which the wave nature of light is noticeable? 

Suggestions for Some More Experiments 

1. Examine Ught diffracted by a circular hole 
instead of by a narrow slit. The light source 
should now be a small point, such as a distant 
flashlight bulb. Look also for the interference 
effect with light that passes through two small 
circular sources — pinholes in a card — instead 
of the two narrow slits. (Thomas Young used 
circular openings rather than slits in his orig- 
inal experiment in 1802.) 

2. Look for the diffraction of light by an ob- 
stacle. For example, use straight wires of 
various diameters, parallel to a narrow light 
source. Or use circular objects such as tiny 
spheres, the head of a pin, etc., and a point 
source of light. You can use either method of 
observation — the translucent tape screen, or 
the magnifier. You may have to hold the mag- 
nifier fairly close to the diffracting obstacle. 

Instructions on how to photograph some 
of these effects are in the activities that follow. 



ACTIVITIES 



THIN FILM INTERFERENCE 

Take two clean microscope slides and press 
them together. Look at the Ught they reflect 
from a source (hke a mercury lamp or sodium 
flame) that emits light at only a few definite 
wavelengths. What you see is the result of 
interference between light waves reflected at 
the two inside surfaces which are almost, but 
not quite, touching. (The thin film is the layer 
of air between the slides.) 

This phenomenon can also be used to 
determine the flatness of surfaces. If the two 
inside surfaces are planes, the interference 
fringes are parallel bands. Bumps or depres- 
sions as small as a fraction of a wavelength 
of light can be detected as wiggles in the 
fringes. This method is used to measure very 
small distances in terms of the known wave- 
length of light of a particular color. If two very 
flat sides are placed at a slight angle to each 
other, an interference band appears for every 
wavelength of separation. (Fig. 13-11) 

How could this phenomenon be used to 
measure the thickness of a very fine hair or 
very thin plastic? 



<i/. in+erfersnce bc^ds 




Fig. 13-11 

An alternative is to focus an ordinary 
camera on "infinity" and place it directly be- 
hind the magnifier, using the same setup as 
described in Suggestions for Some More Ex- 
periments on page 237. 

HANDKERCHIEF DIFFRACTION GRATING 

Stretch a Unen or cotton handkerchief of good 
quality and look through it at a distant light 
source, such as a street light about one block 
away. You will see an interesting diffraction 
pattern. (A window screen or cloth umbrella 
will also work.) 



PHOTOGRAPHING DIFFRACTION 
PATTERNS 

Diffraction patterns like those pictured here 
can be produced in your lab or at home. The 
photos in Figs. 13-12 and 13-13 were produced 
with the setup diagrammed in Fig. 13-14. 



light source 



Screen ov^ 
Trim pouck 



object 



I J' m -^ 



1 2 "^ - - 



Fig. 13-12 





Fig. 13-13 




Fig. 13-14 



Activities 



139 



To photograph the patterns, you must have 
a darkroom or a large, hght-tight box. Figure 
13-13 was taken using a Polaroid 4X5 back 
on a Graphic press camera. The lens was re- 
moved, and a single sheet of 3000-ASA-speed 
Polaroid film was exposed for 10 seconds; a 
piece of cardboard in front of the camera was 
used as a shutter. 

As a light source, use a iT-volt flashlight 
bulb and AA cell. Turn the bulb so the end of 
the filament acts as a point source. A red (or 
blue) filter makes the fringes sharper. You 
can see the fringes by examining the shadow 
on the screen with the lOx magnifier. Razor 
blades, needles, or wire screens make good 
objects. 

POISSON'S SPOT 

A bright spot can be observed in a photograph 
of the center of some shadows, like that shown 
in the photograph. Fig. 13-15. To see this. 




Fig. 13-15 

set up a light source, obstacle, and screen 
as shown in Fig. 13-16. Satisfactory results 
require complete darkness. Try a two-second 
exposure with Polaroid 3000-ASA-film. 




r-i 



ls»- 






V 



Fig. 13-16 



Small B8 ce,^^^r<^d 
to o,ia&s s'id*. 



PHOTOGRAPHIC ACTIVITIES 

The number of photography activities is 
limitless, so we shall not try to describe many 
in detail. Rather, this is a collection of sugges- 
tions to give you a "jumping-off^' point for 
classroom displays, demonstrations, and cre- 
ative work. 

(a) History of photography 

Life magazine, December 23, 1966, had an 
excellent special issue on photography. How 
the world's first trichromatic color photograph 
was made by James Clerk Maxwell in 1861 
is described in the Science Study Series paper- 
back. Latent Image, by Beaumont Newhall. 
Much of the early history of photography in 
the United States is discussed in Mathew 
Brady, by James D. Horan, Crown Publishers. 

(b) Schlieren photography 

For a description and instructions for equip- 
ment, see Scientific American, February 1964, 
p. 132-3. 

(c) Infrared photography 

Try to make some photos like that shown on 
page 14 of your Unit 4 Text. Kodak infrared 
film is no more expensive than normal black 
and white film, and can be developed with 
normal developers. If you have a 4 x 5 camera 
with a Polaroid back, you can use 4X5 Polar- 
oid infrared film sheets. You may find the 
Kodak Data Book M-3, "Infrared and Ultra- 
violet Photography," very helpful. 

COLOR 

One can easily carry out many intriguing ex- 
periments and activities related to the physi- 
cal, physiological, and psychological aspects 
of color. Some of these are suggested here. 

(a) Scattered light 

Add about a quarter-teaspoon of milk to a 
drinking glass full of water. Set a flashlight 
about two feet away so it shines into the glass. 
When you look through the milky water toward 
the light, it has a pale orange color. As you 
move around the glass, the milky water ap- 
pears to change color. Describe the change and 
explain what causes it. 

(b) The rainbow effect 

The way in which rainbows are produced can 
be demonstrated by using a glass of water as a 



140 



Activities 



large cylindrical raindrop. Place the glass on 
a piece of white paper in the early morning or 
late afternoon sunlight. To make the rainbow 
more visible, place two books upright, leaving 
a space a little wider than the glass between 
them, so that the sun shines on the glass but 
the white paper is shaded (Fig. 13-17). The 
rainbow will be seen on the backs of the books. 
What is the relationship between the arrange- 
ment of colors of the rainbow and the side of 
the glass that the light entered? This and other 
interesting optical effects are described in 
Science for the Airplane Passenger, by Eliza- 
beth A. Wood, Houghton-Mifflin Co., 1968. 




Fig. 13-17 

(c) Color vision by contrast (Land effect) 
Hook up two small lamps as shown in Fig. 
13-18. Place an obstacle in front of the screen 

-filter 

obstacle iv. Screen 





Fig. 13-18 

so that adjacent shadows are formed on the 
screen. Do the shadows have any tinge of 
color? Now cover one bulb with a red filter 
and notice that the other shadow appears 
green by contrast. Try this with different 
colored filters and vary the light intensity by 
moving the lamps to various distances, 
(d) Land two-color demonstrations 
A different and interesting activity is to demon- 
strate that a full-color picture can be created 
by simultaneously projecting two black-and- 
white transparencies taken through a red and 
a green filter. For more information see Sci- 
entific American, May 1959; September 1959; 
and January 1960. 



POLARIZED LIGHT 

The use of polarized light in basic research 
is spreading rapidly in many fields of science. 
The laser, our most intense laboratory source 
of polarized light, was invented by researchers 
in electronics and microwaves. Botanists have 
discovered that the direction of growth of 
certain plants can be determined by control- 
ling the polarization form of illumination, and 
zoologists have found that bees, ants, and 
various other creatures routinely use the 
polarization of sky light as a navigational 
"compass." High-energy physicists have found 
that the most modem particle accelerator, the 
synchrotron, is a superb source of polarized 
x-rays. Astronomers find that the polarization 
of radio waves from planets and from stars 
offers important clues as to the dynamics of 
those bodies. Chemists and mechanical engi- 
neers are finding new uses for polarized light 
as an analytical tool. Theoreticians have dis- 
covered shortcut methods of dealing with 
polarized light algebraically. From all sides, 
the onrush of new ideas is imparting new vigor 
to this classical subject. 

A discussion of many of these aspects of 
the nature and application of polarized light, 
including activities such as those discussed 
below, can be found in Polarized Light, by 
W. A. ShurcUff and S. S. Ballard, Van Nostrand 
Momentum Book #7. 1964. 
(a) Detection 

Polarized light can be detected directly by the 
unaided human eye, provided one knows what 
to look for. To develop this ability, begin by 
staring through a sheet of Polaroid at the sky 
for about ten seconds. Then quickly turn the 
polarizer 90° and look for a pale yellow brush- 
shaped pattern similar to the sketch in Fig. 
13-19. 




-^e£^^■ 3 iJESHees- 



Fig. 13-19 



Activities 



141 



The color will fade in a few seconds, but 
another pattern will appear when the Polaroid 
is again rotated 90°. A light blue filter behind 
the Polaroid may help. 

How is the axis of the brush related to the 
direction of polarization of light transmitted 
by the Polaroid? (To determine the polarization 
direction of the filter, look at light reflected 
from a horizontal non-metallic surface, such 
as a table top. Turn the Polaroid until the re- 
flected light is brightest. Put tape on one edge 
of the Polaroid parallel to the floor to show the 
direction of polarization.) Does the axis of the 
yellow pattern always make the same angle 
with the axis of polarization? 

Some people see the brush most clearly 
when viewed with circularly polarized light. 
To make a circular polarizer, place a piece of 
Polaroid in contact with a piece of cellophane 
with its axis of polarization at a 45° angle to 
the fine stretch lines of the cellophane, 
(b) Picket fence analogy 

At some time you may have had polarization 
of light explained to you in terms of a rope 
tied to a fixed object at one end, and being 
shaken at the other end. In between, the rope 
passes through two picket fences (as in Fig. 
13-20), or through two slotted pieces of card- 
board. This analogy suggests that when the 
slots are parallel the wave passes through, 
but when the slots are perpendicular the waves 
are stopped. (You may want to use a rope and 
slotted boards to see if this really happens.) 

Place two Polaroid filters parallel to each 




Fig. 13-20 

other and turn one so that it blacks out the light 
completely. Then place a third filter between 
the first two, and rotate it about the axis of all 
three. What happens? Does the picket fence 
analogy still hold? 

A similar experiment can be done with 
microwaves using parallel strips of tinfoil 
on cardboard instead of Polaroid filters. 

MAKE AN ICE LENS 

Dr. Clawbonny, in Jules Verne's The Adven- 
tures of Captain Hatteras, was able to light 
a fire in -48° weather (thereby saving stranded 
travelers) by shaping a piece of ice into a lens 
and focusing it on some tinder. If ice is clear, 
the sun's rays pass through with little scatter- 
ing. You can make an ice lens by freezing 
water in a round-bottomed bowl. Use boiled, 
distilled water, if possible, to minimize prob- 
lems due to gas bubbles in the ice. Measure the 
focal length of the lens and relate this length 
to the radius of the bowl. (Adapted from 
Physics for Entertainment, Y. Perelman, 
Foreign Languages Publishing House, Mos- 
cow, 1936.) 



B.C. 



By John Hart 



r I \A/0NDgR«FW6ALL. 
SEE CCLORS-THE SAME> 

7. ' ■■< 




..LlKE,..SPgEN 
To\bO Ml&y\T LOOK 

TP<OU&H I CALL ir 

GReeM Tool 




By permission of John Hart and Field Enterprises Inc. 



oK.,..wMAr 
coLCR le 

THAT POCK 
ToroU? 




Chapter 



14 



Electric and Magnetic Fields 



EXPERIMENT 34 ELECTRIC FORCES I 

If you walk across a carpet on a dry day and 
then touch a metal doorknob, a spark may 
jump across between your fingers and the 
knob. Your hair may crackle as you comb it. 
You have probably noticed other examples of 
the electrical effect of rubbing two objects 
together. Does your hair ever stand on end 
after you pull off your clothes over your head? 
(This effect is particuarly strong if the clothes 
are made of nylon, or another synthetic fiber.) 




your finger leaving an inch or so loose as a 
handle. Carefully remove the tape from the 
table by pulling on this loose end, preventing 
the tape from curling up around your fingers. 

To test whether or not the tape became 
electrically charged when you stripped it from 
the table, see if the non-sticky side will pick 
up a scrap of paper. Even better, will the paper 
jump up from the table to the tape? 
Ql Is the tape charged? Is the paper charged? 

So far you have considered only the effect 
of a charged object (the tape) on an uncharged 
object (the scrap of paper). What effect does a 
charged object have on another charged 
object? Here is one way to test it. 

Charge a piece of tape by sticking it to 
the table and peeling it off as you did before. 
Suspend the tape from a horizontal wood rod, 
or over the edge of the table. (Don't let the 
lower end curl around the table legs.) 

Now charge a second strip of tape in the 
same way and bring it close to the first one. 
It's a good idea to have the two non-sticky 
sides facing. 



Small pieces of paper are attracted to a 
plastic comb or ruler that has been rubbed on 
a piece of cloth. Try it. The attractive force 
is often large enough to hft scraps of paper off 
the table, showing that it is stronger than the 
gravitational force between the paper and 
the entire earth! 

The force between the rubbed plastic and 
the paper is an electrical force, one of the 
four basic forces of nature. 

In this experiment you will make some 
observations of the nature of the electrical 
force. If you do the next experiment. Electric 
Forces II. you will be able to make quantitative 
measurements of the force. 

Forces between Electrified Objects 

Stick an 8-inch length of transparent tape to 
the tabletop. Press the tape down well with 




Q2 Do the two tapes affect each other? What 
kind of force is it -attractive or repulsive? 

Hang the second tape a few inches away 
from the first one. Proceed as before and elec- 
trify a third piece of tape. Observe the reaction 
between this and your first two tapes. Record 



Experiment 34 



143 



all your observations. Leave only the first tape 
hanging from its support — you will need it 
again shortly. Discard the other two tapes. 

Stick down a new piece of tape (A) on the 
table and stick another tape (B) over it. Press 
them down well. Peel the stuck-together tapes 
from the table. To remove the net charge the 
pair will have picked up, run the nonsticky 
side of the pair over a water pipe or your lips. 
Check the pair with the original test strip to 
be sure the pair is electrically neutral. Now 
carefully pull the two tapes apart. 
Q3 As you separated the tapes did you notice 
any interaction between them (other than that 
due to the adhesive)? 

Q4 Hold one of these tapes in each hand and 
bring them slowly towards each other (non- 
sticky sides facing). What do you observe? 
Q5 Bring first one, then the other of the tapes 
near the original test strip. What happens? 

Mount A and B on the rod or table edge to 
serve as test strips. If you have rods of plastic, 
glass, or rubber available, or a plastic comb, 
ruler, etc., charge each one in turn by rubbing 
on cloth or fur and bring it close to A and 
then B. 

Although you can't prove it from the re- 
sults of a limited number of experiments, 
there seem to be only two classes of electrified 
objects. No one has ever produced an electri- 
fied object that either attracts or repels both 
A and B (where A and B are themselves elec- 
trified objects. The two classes are called 
positive (+) and negative (— ). Write out a gen- 
eral statement summarizing how all members 
of the same class behave with each other 
(attract, repel, or remain unaffected by) and 
with all members of the other class. 

A Puzzle 

Your system of two classes of electrified ob- 
jects was based on observations of the way 



charged objects interact. But how can you 
account for the fact that a charged object 
(like a rubbed comb) will attract an uncharged 
object (like a scrap of paper)? Is the force 
between a charged body (either + or — ) and an 
uncharged body always attractive, always re- 
pulsive, or is it sometimes one, sometimes 
the other? 

Q6 Can you explain how a force arises 
between charged and uncharged bodies and 
why it is always the way it is? The clue here 
is the fact that the negative charges can 
move about slightly — even in materials called 
non-conductors, like plastic and paper (see 
Sec. 14.5 Text). 




144 



EXPERIMENT 35 

ELECTRIC FORCES II -COULOMB'S LAW 

You have seen that electrically charged ob- 
jects exert forces on each other, but so far 
your observations have been qualitative; you 
have looked but not measured. In this experi- 
ment you will find out how the amount of 
electrical force between two charged bodies 
depends on the amounts of charge and on the 
separation of the bodies. In addition, you will 
experience some of the difficulties in using 
sensitive equipment. 

The electric forces between charges that 
you can conveniently produce in a laboratory 
are small. To measure them at all requires 
a sensitive balance. 

Constructing the Balance 

(If your balance is already assembled, you need 
not read this section — go on to "Using the 
balance.") A satisfactory balance is shown 
in Fig. 14-1. 

Coat a small foam-plastic ball with a con- 
ducting paint and fix it to the end of a plastic 
sliver or toothpick by stabbing the pointed end 
into the ball. Since it is very important that 
the plastic be clean and dry (to reduce leakage 
of charge along the surface); handle the 
plastic slivers as little as possible, and then 
only with clean, dry fingers. Push the sliver 
into one end of a soda straw leaving at least 
an inch of plastic exposed, as shown at the top 
of Fig. 14-2. 

Next, fill the plastic support for the bal- 
ance with glycerin, or oil, or some other liquid. 
Cut a shallow notch in the top of the straw 
about 2 cm from the axle on the side away 
from the sphere — see Fig. 14-2. 




swings ^ -- ' 



Fig. 14-2 



Locate the balance point of the straw, 
ball, and sliver unit. Push a pin through the 
straw at this point to form an axle. Push a 
second pin through the straw directly in front 
of the axle and perpendicular to it. (As the 
straw rocks back and forth, this pin moves 
through the fluid in the support tube. The 
fluid reduces the swings of the balance.) Place 
the straw on the support, the pin hanging down 
inside the vial. Now adjust the balance, by 
sliding the plastic sliver slightly in or out of 
the straw, until the straw rests horizontally. 
If necessary, stick small bits of tape to the 
straw to make it balance. Make sure the bal- 
ance can swing freely while making this 
adjustment. 

Finally, cut five or six small, equal lengths 
of thin, bare wire (such as #30 copper). Each 
should be about 2 cm long, and they must all 
be as close to the same length as you can 
make them. Bend them into small hooks 
(Fig. 14-2) which can be hung over the notch 
in the straw or hung from each other. These 
are your "weights." 

Mount another coated ball on a pointed 
plastic sliver and fix it in a clamp on a ring 
stand, as shown in Fig. 14-1. 




Fig. 14-1 



Experiment 35 



145 



Using the Balance 

Charge both balls by wiping them with a 
rubbed plastic strip. Then bring the ring- 
stand ball down from above toward the bal- 
ance ball. 

Ql What evidence have you that there is a 
force between the two balls? 
Q2 Can you tell that it is a force due to the 
charges? 

Q3 Can you compare the size of electrical 
force between the two balls with the size of 
gravitational force between them? 

Your balance is now ready, but in order to 
do the experiment, you need to solve two tech- 
nical problems. During the experiment you 
will adjust the position of the ring-stand 
sphere so that the force between the charged 
spheres is balanced by the wire weights. The 
straw will then be horizontal. First, therefore, 
you must check quickly to be sure that the 
straw is balanced horizontally each time. 
Second, measure the distance between the 
centers of the two balls, yet you cannot put a 
ruler near the charged balls, or its presence 
will affect your results. And if the ruler isn't 
close to the spheres, it is very difficult to make 
the measurement accurately. 

Here is a way to make the measurement. 
With the balance in its horizontal position, you 
can record its balanced position with a mark 
on a folded card placed near the end of the 
straw (at least 5 cm away from the charges) 
(See Fig. 14-1.) 

How can you avoid the parallax problem? 
Try to devise a method for measuring the 
distance between the centers of the spheres. 
Ask your teacher if you cannot think of one. 
You are now ready to make measurements 
to see how the force between the two balls 
depends on their separation and on their 
charge. 



Doing the Experiment 

From now on, work as quickly as possible but 
move carefully to avoid disturbing the balance 
or creating air currents. It is not necessary to 
wait for the straw to stop moving before you 
record its position. When it is swinging slightly. 



but equally, to either side of the balanced 
position, you can consider it balanced. 

Charge both balls, touch them together 
briefly, and move the ring-stand ball until the 
straw is returned to the balanced position. The 
weight of one hook now balances the electric 
force between the charged spheres at this 
separation. Record the distance between 
the balls. 

Without recharging the balls, add a second 
hook and readjust the system until balance is 
again restored. Record this new position. Re- 
peat until you have used all the hooks -but 
don't reduce the air space between the balls to 
less than 7 cm. Then quickly retrace your steps 
by removing one (or more) hooks at a time and 
raising the ring-stand ball each time to re- 
store balance. 

Q4 The separations recorded on the "return 
trip" may not agree with your previous mea- 
surements with this same number of hooks. 
If they do not, can you suggest a reason why? 
Q5 Why must you not recharge the balls 
between one reading and the next? 

Interpreting Your Results 

Make a graph of your measurements of force 

F against separation d between centers. 

Clearly F and d are inversely related; that is, 

F increases as d decreases. You can go further 

to find the relationship between F and d. For 

example, it might be F ^ i/d, F <^ l/d^ or F c^ 

l/d^ etc. 

Q6 How would you test which of these best 

represents your results? 

Q7 What is the actual relationship between 

F and d? 

Further Investigation 

In another experiment you can find how the 
force F varies with the charges on the spheres, 
when d is kept constant. 

Charge both balls and then touch them 
together briefly. Since they are nearly iden- 
tical, it is assumed that when touched, they 
will share the total charge almost equally. 

Hang four hooks on the balance and move 
the ring-stand ball until the straw is in the 
balanced position. Note this position. 



146 



Experiment 35 



Touch the upper ball with your finger to 
discharge the ball. If the two balls are again 
brought into contact, the charge left on the 
balance ball will be shared equally between 
the two balls. 

Q8 What is the charge on each ball now (as 
a fraction of the original charge)? 

Return the ring-stand ball to its previous 
position and find how many hooks you must 
remove to restore the balance. 
Q9 Can you state this result as a mathemati- 



cal relationship between quantity of charge 
and magnitude of force? 

QIO Consider why you had to follow two 
precautions in doing the experiment: 

(a) Why can a ruler placed too close to the 
charge affect results? 

(b) Why was it suggested that you get the 
spheres no closer than about 2^ cm? 

Qll How might you modify this experiment 
to see if Newton's third law applies to these 
electric forces? 




Experiment 36 



147 



EXPERIMENT 36 
FORCES ON CURRENTS 

If you did Experiment 35. you used a simple 
but sensitive balance to investigate how the 
electric force between two charged bodies 
depends on the distance between them and on 
the amount of charge. In this and the next 
experiment you will examine a related effect: 
the force between moving charges — that is, 
between electric currents. You will investigate 
the effect of the magnitudes and the directions 
of the currents. Before starting the experiment 
you should have read the description of Oer- 
sted and Ampere's work (Text Sec. 14.11 and 
Sec. 14.12). 




Fig. 14-3 

The apparatus for these experiments (like 
that in Fig. 14-3) is similar in principle to the 
balance apparatus you used to measure elec- 
tric forces. The current balance measures the 
force on a horizontal rod suspended so that it 
is free to move in a horizontal direction at right 
angles to its length. You can study the forces 
exerted by a magnetic field on a current by 
bringing a magnet up to this rod while there is 
a current in it. A force on the current-carrying 
rod causes it to swing away from its original 
position. 

You can also pass a current through a fixed 
wire parallel to the pivoted rod. Any force ex- 
erted on the rod by the current in the fixed wire 



will again cause the pivoted rod to move. You 
can measure these forces simply by measuring 
the counter force needed to return the rod to 
its original position. 

Adjusting the Current Balance 

This instrument is more complicated than 
those most of you have worked with so far. 
Therefore it is worthwhile spending a little 
time getting to know how the instrument 
operates before you start taking readings. 

1. You have three or four light metal rods 

bent into I ) or '-u-^ shapes. These are 

the movable "loops." Set up the balance with 
the longest loop clipped to the pivoted hori- 
zontal bar. Adjust the loop so that the horizon- 
tal part of the loop hangs level with the bundle 
of wires (the fixed coil) on the pegboard frame. 
Adjust the balance on the frame so that the 
loop and coil are parallel as you look down at 
them. They should be at least five centimeters 
apart. Make sure the loop swings freely. 

2. Adjust the "counterweight" cylinder to 
balance the system so that the long pointer 
arm is approximately horizontal. Mount the 
S -shaped plate (zero-mark indicator) 
in a clamp and position the plate so that the 
zero line is opposite the horizontal pointer 
(Fig. 14-4). (If you are using the equipment 
for the first time, draw the zero-index line 
yourself.) 




Fig. 14-4 Set the zero mark level with the pointer when 
there is current in the balance loop and no current 
in the fixed coil. (See large photo on Handbook 4 cover.) 

3. Now set the balance for maximum sensi- 
tivity. To do this, move the sensitivity clip up 
the vertical rod (Fig. 14-5) until the loop slowly 
swings back and forth. These oscillations may 
take as much as four or five seconds per swing. 
If the clip is raised too far. the balance may 



148 



Experiment 36 




Fig. 14-5 

become unstable and flop to either side with- 
out "righting" itself. 

4. Connect a 6V 5 amp max power supply that 
can supply up to 5 amps through an ammeter 
to one of the flat horizontal plates on which the 
pivots rest. Connect the other plate to the 
other terminal of the power supply. (Fig. 14.6.) 




Fig. 14-6 

To limit the current and keep it from tripping 
the circuit-breaker, it may be necessary to put 
one or two 1-ohm resisters in the circuit. (If 
your power supply does not have variable con- 
trol, it should be connected to the plate through 
a rheostat.) 

5. Set the variable control for minimum cur- 
rent, and turn on the power supply. If the am- 
meter deflects the wrong way, interchange the 
leads to it. Slowly increase the current up to 
about 4.5 amps. 



6. Now bring a small magnet close to the 
pivoted conductor. 

Ql How must the magnet be placed to have 
the biggest effect on the rod? What determines 
the direction in which the rod swings? 

You will make quantitative measurements 
of the forces between magnet and current in 
the next experiment, "Currents, Magnets, 
and Forces." The rest of this experiment is 
concerned with the interaction between two 
currents. 

7. Connect a similar circuit — power supply, 
ammeter, and rheostat (if no variable control 
on the power supply) — to the fixed coU on the 
vertical pegboard-the bundle of ten wires, 
not the single wire. The two circuits (fixed coU 
and movable hook) must be independent. Your 
setup should now look like the one shown in 
Fig. 14.7. Only one meter is actually required, 
as you can move it from one circuit to the other 
as needed. It is. however, more convenient to 
work with two meters. 




(DJ 

■'nmmeren 



' ffHEaTrf 



Fig. 14-7 Current balance connections using rheo- 
stats when variable power supply is not available. 

8. Turn on the currents in both circuits and 
check to see which way the pointer rod on the 
balance swings. It should move uip. If it does 
not, see if you can make the pointer swing wp 
by changing something in your setup. 

Q2 Do currents flowing in the same direction 
attract or repel each other? What about cur- 
rents flowing in opposite directions? 

9. Prepare some "weights" from the thin wire 
given to you. You will need a set that contains 
wire lengths of 1 cm, 2 cm. 5 cm, and 10 cm. 
You may want more than one of each but you 
can make more as needed during the experi- 
ment. Bend them into small S-shaped hooks 
so that they can hang from the notch on the 



Experiment 36 



149 



pointer or from each other. This notch is the 
same distance from the axis of the balance as 
the bottom of the loop so that when there is a 
force on the horizontal section of the loop, the 
total weight F hung at the notch will equal the 
magnetic force acting horizontally on the loop. 
(See Fig. 14-8.) 



hooks 



psfcrD- 



F <- 



loop 



Fig. 14-8 Side view of a balanced loop. The distance 
from the pivot to the w^ire hook is the same as the 
distance to the horizontal section of the loop, so the 
weight of the additional wire hooks is equal in magni- 
tude to the horizontal magnetic force on the loop. 



These preliminary adjustments are com- 
mon to all the investigations. But from here on 
there are separate instructions on three differ- 
ent experiments. Different members of the 
class will investigate how the force depends 
upon: 

(a) the current in the wires, 

(b) the distance between the wires, or 

(c) the length of one of the wires. 

When you have finished your experiment — 
(a), (b), or (c) — read the section "For class 
discussion." 

(a) How Force Depends on Current in 
the Wires 

By keeping a constant separation between the 
loop and the coil, you can investigate the ef- 
fects of varying the currents. Set the balance 
on the frame so that, as you look down at them, 
the loop and the coil are parallel and about 
1.0 cm apart. 

Set the current in the balance loop to about 
3 amps. Do not change this current throughout 
the experiment. With this cuirent in the bal- 



ance loop and no current in the fixed coil, set 
the zero-mark in line with the pointer rod. 

Starting with a relatively small current in 
the fixed coU (about 1 amp), find how many 
centimeters of wire you must hang on the 
pointer notch untU the pointer rod returns to 
the zero mark. 

Record the current If in the fixed coil 
and the length of wire added to the pointer 
arm. The weight of wire is the balancing 
force F. 

Increase I, step by step, checking the cur- 
rent in the balance loop as you do so until you 
reach currents of about 5 amps in the fixed coil. 
Q3 What is the relationship between the cur- 
rent in the fixed coil and the force on the bal- 
ance loop? One way to discover this is to plot 
force F against current If. Another way is to 
find what happens to the balancing force when 
you double, then triple, the current If. 
Q4 Suppose you had held If constant and 
measured F as you varied the current in the 
balance loop 1^,. What relationship do you think 
you would have found between F and lb? 
Check your answer experimentally (say, by 
doubling I^) if you have time. 
Q5 Can you write a symbolic expression for 
how F depends on both If and lb? Check your 
answer experimentally (say by doubling both 
If and lb), if you have time. 
Q6 How do you convert the force, as mea- 
sured in centimeters of wire hung on the 
pointer arm, into the conventional units for 
force in new tons? 

(b) How Force Varies With the Distance 
Between Wires 

To measure the distance between the two 
wires, you have to look down. Put a scale on 
the wooden shelf below the loop. Because there 
is a gap between the wires and the scale, the 
number you read on the scale changes as you 
move your head back and forth. This effect 
is called parallax, and it must be reduced if 
you are to get good measurements. If you look 
down into a minor set on the shelf, you can 
tell when you are looking straight down be- 
cause the wire and its image will line up. Try 
it. (Fig. 14-9.) 



150 



Experiment 36 




a_fnirror 



imtje s 



Fig. 14-9 Only when your eye is perpendicularly above 
the moving wire will it line up with its reflection in 
the mirror. 

Stick a length of centimeter tape along the 
side of the mirror so that you can sight down 
and read off the distance between one edge of 
the fixed wire and the corresponding edge of 
the balance loop. Set the zero mark with a 
current I^, of about 4.5 amps in the balance 
loop and no current Z, in the fixed coil. Then 
adjust the distance to about 0.5 cm. 

Begin the experiment by adjusting the 
current passing through the fixed coil to 4.5 
amps. Hang weights on the notch in the pointer 
arm until the pointer is again at the zero posi- 
tion. Record the weight and distance carefully. 

Repeat your measurements for four or 
five greater separations. Between each set of 
measurements make sure the loop and coil are 
still parallel; check the zero position, and see 
that the currents are still 4.5 amps. 
Q7 What is the relationship between the 
force E on the balance loop and the distance 
d between the loop and the fixed coil? One way 
to discover this is to find some function of d 
(such as 1/d^, 1/d. d^, etc.) which gives a straight 
line when plotted against F. Another way is to 
find what happens to the balancing force F 
when you double, then triple, the distance d. 
Q8 If the force on the balance loop is F, what 
is the force on the fixed coil? 
Q9 Can you convert the force, as measured 
in centimeters of wire hung on the pointer 
arm. into force in newtons? 

(c) How Force Varies With the Length of 
One of the Wires 

By keeping constant currents I, and It, and a 
constant separation d, you can investigate the 
effects of the length of the wires. In the cur- 



rent balance setup it is the bottom, horizontal 
section of the loop which interacts most 
strongly with the coil and loops with several 
different lengths of horizontal segment are 
provided. 

To measure the distances between the two 
wires, you have to look down on them. Put a 
scale on the wooden shelf below the loop. Be- 
cause there is a gap between the wires and the 
scale, what you read on the scale changes as 
you move your head back and forth. This effect 
is called paraUax, and parallax must be re- 
duced if you are to get good measurements. 
If you look down into a mirror set on the shelf, 
you can tell when you are looking straight 
down because the wire and its image will line 
up. Try^ it. (Fig. 14-9.) 

Stick a length of centimeter tape along the 
side of the miiTor. Then you can sight down 
and read off the distance between one edge of 
the fixed wire and the corresponding edge of 
the balance loop. Adjust the distance to about 
0.5 cm. With a current /h of about 4.5 amps in 
the balance loop and no current If in the fixed 
coil, set the pointer at the zero mark. 

Begin the experiment by passing 4.5 amps 
through both the balance loop and the fixed 
coil. Hang weights on the notch in the pointer 
in the pointer arm until the pointer is again 
at the zero position. 

Record the value of the currents, the 
distance between the two wires, and the 
weights added. 

Turn off the currents, and carefully re- 
move the balance loop by sliding it out of the 
holding clips. (Fig. 14-10.) Measure the length 
I of the horizontal segment of the loop. 



Fig. 14-10 




Experiment 36 



151 



Insert another loop. Adjust it so that it 
is level with the fixed coil and so that the dis- 
tance between loop and coil is just the same 
as you had before. This is important. The loop 
must also be parallel to the fixed coil, both as 
you look down at the wires from above and as 
you look at them from the side. Also reset the 
clip on the balance for maximum sensitivity. 
Check the zero position, and see that the cur- 
rents are still 4.5 amps. 

Repeat your measurements for each bal- 
ance loop. 

QIO What is the relationship between the 
length I of the loop and the force F on it? 
One way to discover this is to find some func- 
tion of I (such as I, 1-, 111, etc.) that gives a 
straight line when plotted against F. Another 
way is to find what happens to F when you 
double I. 

Ql 1 Can you convert the force, as measured 
in centimeters of wire hung on the pointer arm, 
into force in newtons? 

Q12 If the force on the balance loop is F, 
what is the force on the fixed coil? 



For Class Discussion 

Be prepared to report the results of your par- 
ticular investigation to the rest of the class. 
As a class you will be able to combine the in- 
dividual experiments into a single statement 
about how the force varies with current, with 
distance, and with length. In each part of this 
experiment, one factor was varied whUe the 
other two were kept constant. In combining 
the three separate findings into a single ex- 
pression for force, you are assuming that the 
effects of the three factors are independent. 
For example, you are assuming doubling one 
current will always double the force -regard- 
less of what constant values d and I have. 
Ql 3 What reasons can you give for assuming 
such a simple independence of effects? What 
could you do experimentally to support the 
assumption? 

Q14 To make this statement into an equation, 
what other facts do you need -that is, to be 
able to predict the force (in newtons) existing 
between the currents in two wires of given 
length and separation? 



152 



EXPERIMENT 37 

CURRENTS, MAGNETS, AND FORCES 

If you did the last experiment, "Forces on 
Currents," you found how the force between 
two wires depends on the current in them, 
their length, and the distance between them. 
You also know that a nearby magnet exerts a 
force on a current-carrying wire. In this ex- 
periment you will use the current balance to 
study further the interaction between a mag- 
net and a current-carrying wire. You may need 
to refer back to the notes on Experiment 36 
for details on the equipment. 

In this experiment you will not use the 
fixed coil. The frame on which the coil is 
wound will serve merely as a convenient sup- 
port for the balance and the magnets. 

Attach the longest of the balance loops 
to the pivotal horizontal bar, and connect it 
through an ammeter to a variable source of 
current. Hang weights on the pointer notch 
untU the pointer rod returns to the zero mark. 
(See Fig. 14-11.) 



hooks 



T 



SWJ 



F <- 



loot 



Fig. 14-11 Side view of a balanced loop. Since the 
distance from the pivot to the wire hooks is the same 
as the distance to the horizontal section of the loop, 
the weight of the additional wire hooks is equal to the 
horizontal magnetic force on the loop. 



(a) How the Force Between Current and 
Magnet Depends On the Current 

1. Place two small ceramic magnets on the 
inside of the iron yoke. Their orientation is 
important; they must be turned so that the two 
near faces attract each other when they are 
moved close together. (Careful: Ceramic mag- 
nets are brittle. They break if you drop them.) 
Place the yoke and magnet unit on the plat- 




form so that the balance loop passes through 
the center of the region between the ceramic 
magnets. (Fig. 14-12.) 



balance loop 



^^ pole piece 

Fig. 14-12 Each magnet consists of a yoke and a pair 
of removable ceramic-magnet pole pieces. 

2. Check whether the horizontal pointer 
moves up when you turn on the current. If 
it moves down, change something (the cur- 
rent? the magnets?) so that the pointer does 
swing up. 

3. With the current off, mark the zero position 
of the pointer arm with the indicator. Adjust 
the current in the coil to about 1 amp. Hang 
wire weights in the notch of the balance arm 
until the pointer returns to the zero position. 

Record the current and the total balancing 
weight. Repeat the measurements for at least 
four greater currents. Retween each pair of 
readings check the zero position of the point- 
er arm. 

Ql What is the relationship between the 
current I,, and the resulting force F that the 
magnet exerts on the wire? (Try plotting a 
graph.) 

Q2 If the magnet exerts a force on the cur- 
rent, do you think the current exerts a force 
on the magnet? How would you test this? 
Q3 How would a stronger or a weaker magnet 
affect the force on the current? If you have 
time, try the experiment with different mag- 
nets or by doubling the number of pole pieces. 
Then plot F against h on the same graph as 
in Ql above. How do the plots compare? 

(b) How the Force Between a Magnet and 
a Current Depends On the Length of the 
Region of Interaction 

1. Place two small ceramic magnets on the 
inside of the iron yoke to act as pole pieces 
(Fig. 14-12). (Careful. Ceramic magnets are 
brittle. They break if you drop them.) Their 
orientation is important; they must be turned 
so that the two near faces attract each other 
when they are moved close together. Place 



Experiment 37 



153 



the yoke and magnet unit on the platform so 
that the balance loop passes through the 
center of the region between the ceramic 
magnets (Fig. 14-12). 

Place the yoke so that the balance loop 
passes through the center of the magnet and 
the pointer moves up when you turn on the 
current. If the pointer moves down, change 
something (the current? the magnets?) so 
that the pointer does swing up. 

With the current off, mark the zero position 
of the pointer with the indicator. 

2. Hang ten or fifteen centimeters of wire on 
the notch in the balance rod, and adjust the 
current to return the pointer rod to its zero 
position. Record the current and the total 
length of wire, and set aside the magnet for 
later use. 

3. Put a second yoke and pair of pole pieces 
in position, and see if the balance is restored. 
You have changed neither the current nor the 
length of wire hanging on the pointer. There- 
fore, if balance is restored, this magnet must 
be of the same strength as the first one. If it 
is not, try other combinations of pole pieces 
until you have two magnets of the same 
strength. If possible, try to get three matched 
magnets. 

4. Now you are ready for the important test. 
Place two of the magnets on the platform at 
the same time (Fig. 14-13). To keep the mag- 
nets from affecting each other's field appreci- 
ably, they should be at least 10 cm apart. Of 
course each magnet must be positioned so the 
pointer is deflected upward. With the current 
just what it was before, hang wire weights in 
the notch until the balance is restored. 



Fig. 14-13 




If you have three magnet units, repeat 
the process using three units at a time. Again, 
keep the units well apart. 



Interpreting Your Data 

Your problem is to find a relationship between 
the length / of the region of interaction and 
the force F on the wire. 

You may not know the exact length of the 
region of interaction between magnet and wire 
for a single unit. It certainly extends beyond 
the region between the two pole pieces. But 
the force decreases rapidly with distance from 
the magnets and so as long as the separate 
units are far from each other, neither will be 
influenced by the presence of the other. You 
can then assume that the total length of inter- 
action with two units is double that for one unit. 
Q4 How does F depend on I? 

(c) A Study of the Interaction Between the 
Earth and an Electric Current 

The magnetic field of the earth is much weaker 
than the field near one of the ceramic magnets, 
and the balance must be adjusted to its maxi- 
mum sensitivity. The following sequence of 
detailed steps will make it easier for you to 
detect and measure the small forces on the loop. 
1. Set the balance, with the longest loop, to 
maximum sensitivity by sliding the sensitivity 
clip to the top of the vertical rod. The sensi- 
tivity can be increased further by adding a 
second clip -but be careful not to make the 
balance top heavy so that it flops over and 
won't swing. 

2. With no current in the balance loop, align 
the zero mark with the end of the pointer arm. 

3. Turn on the current and adjust it to about 
5 amps. Turn off the current and let the bal- 
ance come to rest. 

4. Turn on the current, and observe carefully: 
Does the balance move when you turn the cur- 
rent on? Since there is no current in the fixed 
oil, and there are no magnets nearby, any force 
acting on the current in the loop must be due 
to an interaction between it and the earth's 
magnetic field. 

5. To make measurements of the force on 
the loop, you must set up the experiment so 
that the pointer swings up when you turn on 
the current. If the pointer moves down, try to 
find a way to make it go up. (If you have 
trouble, consult your teacher.) Turn off the 



154 



Experiment 37 



current, and bring the balance to rest. Mark 
the zero position with the indicator. 
6. Turn on the current. Hang weights on the 
notch, and adjust the current to restore bal- 
ance. Record the current and the length of 
wire on the notch. Repeat the measurement 
of the force needed to restore balance for 
several different values of current. 

If you have time, repeat your measure- 
ments of force and current for a shorter loop. 

Interpreting Your Data 

Try to find the relationship between the cur- 
rent lb in the balance loop and the force F on 
it. Make a plot of F against /|,. 
Q5 How can you convert your weight unit 
(say, cm of wire) into newtons of force? 
Q6 What force (in newtons) does the earth's 
magnetic field in your laboratory exert on a 
current h in the loop? 

For Class Discussion 

Different members of the class have investi- 
gated how force F between a current and a 
magnet varies with current / and with the 
length of the region of interaction with the 
current /. It should also be clear that in any 
statement that describes the force on a current 
due to a magnet, you must include another 
term that takes into account the "strength" 
of the magnet. 

Be prepared to report to the class the re- 
sults of your own investigations and to help 



formulate an expression that includes all the 
relevant factors investigated by different 
members of the class. 

Q7 The strength of a magnetic field can be 
expressed in terms of the force exerted on a 
wire carrying 1 amp when the length of the 
wire interacting with the field is 1 meter. Try 
to express the strength of the magnetic field 
of your magnet yoke or of the earth's magnetic 
field in these units, newtons per ampere-meter. 
(That is, what force would the fields exert on 
a horizontal wire 1 meter long carrying a 
current of 1 amp?) 

In using the current balance in this experi- 
ment, all measurements were made in the zero 
position — when the loop was at the very bottom 
of the swing. In this position a vertical force 
will not affect the balance. So you have mea- 
sured only horizontal forces on the bottom 
of the loop. 

But, since the force exerted on a current by 
a magnetic field is always at right angles to 
the field, you have therefore measured only the 
vertical component of the magnetic fields. 
From the symmetry of the magnet yoke, you 
might guess that the field is entirely vertical 
in the region directly between the pole pieces. 
But the earth's magnetic field is exactly verti- 
cal only at the magnetic poles. (See the draw- 
ing on page 68 of the Text.) 
Q8 How would you have to change the ex- 
periment to measure the horizontal component 
of the earth's magnetic field? 





Experiment 38 



155 



EXPERIMENT 38 
ELECTRON BEAM TUBE 
If you did the experiment "Electric Forces II — 
Coulomb's Law," you found that the force 
on a test charge, in the vicinity of a second 
charged body, decreases rapidly as the dis- 
tance between the two charged bodies is 
increased. In other words, the electric field 
strength due to a single small charged body 
decreases with distance from the body. In 
many experiments it is useful to have a region 
where the field is uniform, that is, a region 
where the force on a test charge is the same 
at all points. The field between two closely 
spaced parallel, flat, oppositely charged plates 
is very nearly uniform (as is suggested by the 
behavior of fibers aligned in the electric field 
between two plates shown in Fig. 14-14). 




U 



Fig. 14-14 The field between two parallel flat plates 
is uniform. E =V/d where V is the potential difference 
(volts) between the two plates. 

The nearly uniform magnitude E depends 
upon the potential difference between the 
plates and upon their separation d: 

Besides electric forces on charged bodies, you 
found if you did either of the previous two ex- 
periments with the current balance, you found 
that there is a force on a current-carrying wire 
in a magnetic field. 

Free Charges 

In this experiment the charges will not be 
confined to a foam-plastic ball or to a metallic 
conductor. Instead they will be free charges — 
free to move through the field on their own in 
air at low pressure. 



You will build a special tube for this ex- 
periment. The tube will contain a filament wire 
and a metal can with a small hole in one end. 
Electrons emitted from the heated filament 
are accelerated toward the positively charged 
can and some of them pass through the hole 
into the space beyond, forming a beam of elec- 
trons. It is quite easy to observe how the beam 
is affected by electric and magnetic fields. 

When one of the air molecules remaining 
in the partially evacuated tube is struck by 
an electron, the molecule emits some light. 
Molecules of different gases emit light of dif- 
ferent colors. (Neon gas, for example, glows 
red.) The bluish glow of the air left in the tube 
shows the path of the electron beam. 




Building Your Electron Beam Tube 

Full instructions on how to build the tube are 
included with the parts. Note that one of the 
plates is connected to the can. The other plate 
must not touch the can. 

After you have assembled the filament and 
plates on the pins of the glass tube base, you 
can see how good the alignment is if you look 
in through the narrow glass tube. You should 
be able to see the filament across the center of 
the hole in the can. Don't seal the header in 
the tube until you have checked this align- 
ment. Then leave the tube undisturbed over- 
night while the sealant hardens. 



156 



Experiment 38 




Fig. 14-15 

Operating the Tube 

With the power supply turned OFF. connect 
the tube as shown in Figs. 14-15 and 14-16. 
The low-voltage connection provides current 
to heat the filament and make it emit elec- 
trons. The ammeter in this circuit allows you 
to keep a close check on the current and avoid 
burning out the filament. Be sure the 0-6V 
control is turned down to 0. 

The high-voltage connection provides the 
field that accelerates these electrons toward 
the can. Let the teacher check the circuits 
before you proceed further. 




O-C ojnp 



Fig. 14-16 The pins to the two plates are connected 
together, so that they will be at the same potential and 
there will be no electric field between them. 

Turn on the vacuum pump and let it run 
for several minutes. If you have done a good 
job putting the tube together, and if the 
vacuum pump is in good condition, you should 
not have much difficulty getting a glow in the 
region where the electron beam comes through 
the hole in the can. 

You should work with the faintest glow 
that you can see clearly. Even then, it is im- 



portant to keep a close watch on the brightness 
of the glow. There is an appreciable current 
from the filament wire to the can. As the re- 
sidual gas gets hotter, it becomes a better 
conductor increasing the current. The in- 
creased current will cause further heating, 
and the process can build up -the back end of 
the tube will glow intensely blue-white and the 
can will become red hot. You must immedi- 
ately reduce the current to prevent the gun 
from being destroyed. If the glow in the back 
end of the tube begins to increase noticeably, 
turn down the filament current very quickly, 
or turn off the power supply altogether. 

Deflection by an Electric Field 

When you get an electron beam, try to deflect 
it in an electric field by connecting the deflect- 
ing plate to the ground terminal (See Fig. 
14-17), you will put a potential difference 
between the plates equal to the accelerating 
voltage. Other connections can be made to get 
other voltages, but check your ideas with your 
teacher before trying them. 




Fig. 14-17 Connecting one deflecting plate to ground 
will put a potential difference of 125 V between the 
plates. 



Ql Make a sketch showing the direction 
of the electric field and of the force on the 
charged beam. Does the deflection in the 
electric field confirm that the beam con- 
sists of negatively charged particles? 

Deflection by a Magnetic Field 

Now try to deflect the beam in a magnetic 
field, using the yoke and magnets from the 
current balance experiments. 
Q2 Make a vector sketch showing the direc- 
tion of the magnetic field, the velocity of the 
electrons, and the force on them. 



Experiment 38 



157 



Balancing the Electric and Magnetic Effects 

Try to orient the magnets so as to cancel the 
effect of an electric field between the two 
plates, permitting the charges to travel straight 
through the tube. 

Q3 Make a sketch showing the orientation 
of the magnetic yoke relative to the plates. 

The Speed of the Charges 

As explained in Chapter 14 of the Text, the 
magnitude of the magnetic force is qvB. 
where q is the electron charge, v is its speed, 
and B is the magnetic field strength. The 
magnitude of the electric force is qE. where 
E is the strength of the electric field. If you 
adjust the voltage on the plates until the 
electric force just balances the magnetic 
force, then qvB = qE and therefore v = BIE. 
Q4 Show that B/E will be in speed units if 
B is expressed in newtons/ ampere-meter and £ 
is expressed in newtons/coulomb. Hint: Re- 
member that 1 ampere = 1 coulomb sec. 

If you knew the value of B and £, you could 
calculate the speed of the electron. The value 
of E is easy to find, since in a uniform field 
between parallel plates, E = V/d, where V is 
the potential difference between the plate 
(in volts) and d is the separation of the plates 
(in meters). (The unit volts/meter is equivalent 
to newtons/coulomb.) 

A rough value for the strength of the mag- 
netic field between the poles of the magnet- 
yoke can be obtained as described in the 



experiment, CuiTents, Magnets, and Forces. 

Q5 What value do you get for £ (in volts 

per meter)? 

Q6 What value did you get for B (in newtons 

per ampere-meter)? 

Q7 What value do you calculate for the 

speed of the electrons in the beam? 

An Important Question 

One of the questions facing physicists at the 
end of the nineteenth century was to decide 
on the nature of these "cathode rays" (so- 
called because they are emitted from the 
negative electrode or cathode). One group of 
scientists (mostly German) thought that 
cathode rays were a form of radiation, like 
light, while others (mostly English) thought 
they were streams of particles. J. J. Thomson 
at the Cavendish Laboratory in Cambridge, 
England did experiments much like the one 
described here that showed that the cathode 
rays behaved like particles: the particles now 
called electrons. 

These experiments were of great impor- 
tance in the early development of atomic 
physics. In Unit 5 you will do an experiment 
to determine the ratio of the charge of an 
electron to its mass. 

In the following activities for Chapter 14, 
you will find some suggestions for building 
other kinds of electron tubes, similar to the 
ones used in radios before the invention of 
the transistor. 




ACTIVITIES 



DETECTING ELECTRIC FIELDS 

Many methods can be used to explore the 
shape of electric fields. Two very simple ones 
are described here. 

Gilbert's Versorium 

A sensitive electric "compass" is easily con- 
structed from a toothpick, a needle, and a cork. 
An external electric field induces surface 
charges on the toothpick. The forces on these 
induced charges cause the toothpick to line 
up along the direction of the field. 

To construct the versorium, first bend a 
flat toothpick into a slight arc. When it is 
mounted horizontally, the downward curve at 
the ends will give the toothpick stability by 
lowering its center of gravity below the pivot 
point of the toothpick. With a small nail, drill 
a hole at the balance point almost all the way 
through the pick. Balance the pick horizontally 
on the needle, being sure it is free to swing 
like a compass needle. Try bringing charged 
objects near it. 

For details of Gilbert's and other experi- 
ments, see Holton and Roller, Foundations of 
Modern Physical Science, Chapter 26. 

Charged Ball 

A charged pithball (or conductor-coated plastic 
foam ball) suspended from a stick on a thin 
insulating thread, can be used as a rough indi- 
cator of fields around charged spheres, plates, 
and wires. 

Use a point source of light to project a 
shadow of the thread and ball. The angle be- 
tween the thread and the vertical gives a rough 
measure of the forces. Use the charged pith- 
ball to explore the nearly uniform field near a 
large charged plate suspended by tape strips, 
and the 1/r drop-off' of the field near a long 
charged wire. 

Plastic strips lubbed with cloth are ade- 
quate for charging well insulated spheres, 
plates, or wires. (To prevent leakage of charge 
from the pointed ends of a charged wire, fit 
the ends with small metal spheres. Even a 
smooth small blob of solder at the ends should 
help.) 



VOLTAIC PILE 

Cut twenty or more disks of each of two dif- 
ferent metals. Copper and zinc make a good 
combination. (The round metal "slugs" from 
electrical outlet-box installations can be used 
for zinc disks because of their heavy zinc 
coating.) Pennies and nickels or dimes will 
work, but not as well. Cut pieces of filter paper 
or paper towel to fit in between each pair of 
two metals in contact. Make a pUe of the metal 
disks and the salt-water soaked paper, as Volta 
did. Keep the pile in order; for example, copper- 
paper-zinc, copper-paper-zinc, etc. Connect 
copper wires to the top and bottom ends of 
the pile. Touch the free ends of wires with 
two fingers on one hand. What is the effect? 
Can you increase the effect by moistening your 
fingers? In what other ways can you increase 
the effect? How many disks do you need in 
order to light a flashlight bulb? 

If you have metal fillings in your teeth, 
tr\' biting a piece of aluminum foil. Can you 
explain the sensation? (Adapted from History 
of Science Cases for High Schools, Leo E. 
Klopfer, Science Research Associates, 1966.) 

AN 1le BATTERY 

Using a penny (95 percent copper) and a silver 
dime (90 percent silver) you can make an 11^ 
battery. Cut a one-inch square of filter paper 
or paper towel, dip it in salt solution, and place 
it between the penny and the dime. Connect 
the penny and the dime to the terminals of a 
galvanometer with two lengths of copper wire. 
Does your meter indicate a current? Will the 
battery also produce a current with the penny 
and dime in direct dry contact? 

MEASURING MAGNETIC FIELD 
INTENSITY 

Many important devices used in physics ex- 
periments make use of a uniform magnetic 
field of known intensity. Cyclotrons, bubble 
chambers, and mass spectrometers are ex- 
amples. Use the current balance described in 
Experiments 35 and 36. Measure the magnetic 
field intensity in the space between the pole 
faces of two ceramic disk magnets placed 
close together. Then when you are learning 



Activities 



159 



about radioactivity in Unit 6 you can observe 
the deflection of beta particles as they pass 
through this space, and determine the average 
energy of the particles. 

Bend two strips of thin sheet aluminum or 
copper (not iron), and tape them to two disk 
magnets as shown in the drawing below. 




Be sure that the pole faces of the magnets 
are parallel and are attracting each other (un- 
like poles facing each other). Suspend the 
movable loop of the current balance midway 
between the pole faces. Determine the force 
needed to restore the balance to its initial 
position when a measured current is passed 
through the loop. You learned in Experiment 
36 that there is a simple relationship between 
the magnetic field intensity, the length of the 
part of the loop which is in the field, and the 
current in the loop. It is F = BIl, where F is 
the force on the loop (in newtons). B is the 
magnetic field intensity (in newtons per 
ampere-meter), J is the current (in amperes), 
and I is the length (in meters) of that part of 
the current-carrying loop which is actually in 
the field. With your current balance, you can 
measure F, I, and I, and thus compute B. 

For this activity, you make two simplifying 
assumptions which are not strictly true but 
which enable you to obtain reasonably good 
values for B: (a) the field is fairly uniform 
throughout the space between the poles, and 
(b) the field drops to zero outside this space. 
With these approximations you can use the 
diameter of the magnets as the quantity in 
the above expression. 

Try the same experiment with two disk 



magnets above and two below the loop. How 
does B change? Bend metal strips of diff"erent 
shapes so you can vary the distance between 
pole faces. How does this affect B? 

An older unit of magnetic field intensity 
still often used is the gauss. To convert from 
one unit to the other, use the conversion fac- 
tor, 1 newton /ampere-meter =10 gauss. 

Save your records from this activity so 
you can use the same magnets for measuring 
beta deflection in Unit 6. 

MORE PERPETUAL MOTION MACHINES 

The diagrams in Figs. 14-18 and 14-19 show 
two more of the perpetual motion machines 
discussed by R. Raymond Smedile in his book. 
Perpetual Motion and Modern Research for 
Cheap Power. (See also p. 206 of Unit 3 Hand- 
book.) What is the weakness of the argument 
for each of them? (Also see "Perpetual Motion 
Machines," Stanley W. Angrist, Scientific 
American, January, 1968.) 

In Fig. 14-18, A represents a stationary 
wheel around which is a larger, movable 
wheel, E. On stationary wheel A are placed 
three magnets marked B in the position shown 
in the drawing. On rotary wheel £ are placed 
eight magnets marked D. They are attached to 
eight levers and are securely hinged to wheel 




Fig. 14-18 



160 



Activities 



E at the point marked F. Each magnet is also 
provided with a roller wheel, G, to prevent 
friction as it rolls on the guide marked C. 

Guide C is supposed to push each magnet 
toward the hub of this mechanism as it is being 
carried upward on the left-hand side of the 
mechanism. As each magnet rolls over the top, 
the fixed magnets facing it cause the magnet 
on the wheel to fall over. This creates an over- 
balance of weight on the right of wheel E and 
thus perpetually rotates the wheel in a clock- 
wise direction. 

In Figure 14-19, A represents a wheel in 
which are placed eight hollow tubes marked 
E. In each of the tubes is inserted a magnet. 
B, so that it will slide back and forth. D repre- 
sents a stationary rack in which are anchored 
five magnets as shown in the drawing. Each 
magnet is placed so that it will repel the mag- 
nets in wheel A as it rotates in a clockwise 
direction. Since the magnets in stationary rack 
D will repel those in rotary wheel A, this will 
cause a perpetual overbalance of magnet 
weight on the right side of wheel A. 




Fig. 14-19 



ADDITIONAL ACTIVITIES USING THE 
ELECTRON BEAM TUBE 

1. Focusing the Electron Beam 

A current in a wire coiled around the electron 
tube will produce inside the coil a magnetic 
field parallel to the axis of the tube. (Ring- 



shaped magnets slipped over the tube will 
produce the same kind of field.) An electron 
moving directly along the axis will experience 
no force — its velocity is parallel to the magnetic 
field. But for an electron moving perpendicular 
to the axis, the field is perpendicular to its 
velocity — it will therefore experience a force 
(F = qvB) at right angles to both velocity and 
field. If the curved path of the electron remains 
in the uniform field, it will be a circle. The 
centripetal force F = mv-jR that keeps it in 
the circle is just the magnetic force qvB, so 



qvB 



mv 



where R is the radius of the orbit. In this simple 
case, therefore. 



mv 
qB 



Suppose the electron is moving down the 
tube only slightly off axis, in the presence of a 
field parallel to the axis (Fig. 14-20a). The 
electron's velocity can be thought of as made 
up of two components: an axial portion of t^a 
and a transverse portion (perpendicular to the 
axis) Vi (Fig. 14-20b). Consider these two com- 



m 



(a) (b) 

Fig. 14-20 



(c) 



rd) 



i 



ponents of the electron's velocity indepen- 
dently. You know that the axial component will 
be unaffected -the electron will continue to 
move down the tube with speed v., (Fig. 
14-20c). The transverse component, however, 
is perpendicular to the field, so the electron 
will also move in a circle (Fig. 14-20d). In 
this case. 



R = 






Activities 



161 



The resultant motion — uniform speed 
down the axis plus circular motion perpen- 
dicular to the axis — is a helix, like the thread 
on a bolt (Fig. 14-20e). 

In the absence of any field, electrons 
traveling off-axis would continue toward the 
edge of the tube. In the presence of an axial 
magnetic field, however, the electrons move 
down the tube in helixes — they have been 
focused into a beam. The radius of this beam 
depends on the field strength B and the trans- 
verse velocity f,. 

Wrap heavy-gauge copper wire, such as 
#18, around the electron beam tube (about two 
turns per centimeter) and connect the tube to 
a low-voltage (3-6 volts), high-current source 
to give a noticeable focusing effect. Observe 
the shape of the glow, using different coils and 
currents. (Alternatively, you can vary the 
number and spacing of ring magnets slipped 
over the tube to produce the axial field.) 

2. Reflecting the Electron Beam 

If the pole of a very strong magnet is brought 
near the tube (with great care being taken that 
it doesn't pull the iron mountings of the tube 
toward it), the beam glow will be seen to spiral 
more and more tightly as it enters stronger 
field regions. If the field lines diverge enough, 
the path of beam may start to spiral back. The 
reason for this is suggested in SG 14.32 in 
the Text. 

This kind of reflection operates on particles 
in the radiation belt around the earth as the 
approach of the earth's magnetic poles. (See 
drawing at end of Text Chapter 14.) Such 
reflection is what makes it possible to hold 
tremendously energetic charged particles in 
magnetic "bottles." One kind of coil used to 
produce a "bottle " field appears in the Unit 
5 Text. 

3. Diode and Triode Characteristics 

The construction and function of some elec- 
tronic vacuum tubes is described in the next 
activity, "Inside a Radio Tube." In this section 
are suggestions for how you can explore some 
characteristics of such tubes with your elec- 
tron beam tube materials. 

These experiments are performed at ac- 



celerating voltages below those that cause 

ionization (a visible glow) in the electron beam 

tube. 

(a) Rectification 

Connect an ammeter between the can and 

high-voltage supply to show the direction of 

the current, and to show that there is a current 

only when the can is at a higher potential 

than the filament (Fig. 14.21). 

niilliamiiie'ter 
0-30V0 (MrV- 



0-tY 



Fig. 14-21 

Note that there is a measurable current 
at voltages far below those needed to give a 
visible glow in the tube. Then apply an alter- 
nating potential difference between the can 
and filament (for example, from a Variac). 
Use an oscilloscope to show that the can is 
alternately above and below filament potential. 
Then connect the oscilloscope across a resistor 
in the plate circuit to show that the current 
is only in one direction. (See Fig. 14-22.) 





Fig. 14-22 The one-way-valve (rectification) action of 
a diode can be shown by substituting an AC voltage 
source for the DC accelerating voltage, and connect- 
ing a resistor (about 1000 ohms) in series with it. When 
an oscilloscope is connected as shown by the solid 
lines above, it will indicate the current in the can cir- 
cuit. When the one wire is changed to the connection 
shown by the dashed arrow, the oscilloscope will 
indicate the voltage on the can. 



162 



Activities 



(b) Triode 

The "triode" in the photograph below was 
made with a thin aluminum sheet for the plate 
and nichrome wire for the grid. The filament 
is the original one from the electron beam tube 
kit, and thin aluminum tubing from a hobby 
shop was used for the connections to plate and 
grid. (For reasons lost in the history of vacuum 
tubes, the can is usually called the "plate." 
It is interesting to plot graphs of plate current 
versus filament heating current, and plate 
current versus voltage. Note that these char- 
acteristic curves apply only to voltages too 
low to produce ionization.) With such a triode, 



£:AI^PH0M£5 





Fig. 14-23 

you can plot curves showing triode character- 
istics: plate current against grid voltage, plate 
current against plate voltage. 

0-30Y 



grid coil 



-30 - +30 V ( 
Fig. 14-24 

You can also measure the voltage amplifi- 
cation factor, which describes how large a 
change in plate voltage is produced by a 
change in grid voltage. More precisely, the 
amplification factor, 

when the plate current is kept constant. 

Change the grid voltage by a small amount, 
then adjust the plate voltage until you have 
regained the original plate current. The magni- 
tude of the ratio of these two voltage changes 
is the amplification factor. (Commercial 
vacuum tubes commonly have amplifica- 
tion factors as high as 500.) The tube gave 



Of prox 30V, 




output Signal in plate cifcoA 



/Viput siMiial ■fv t^r'id 



Fig. 14-25 An amplifying circuit 

noticeable amplification in the circuit shown 
in Fig. 14-25 and Fig. 14-26. 



Sianol 




Fig. 14-26 Schematic diagram of amplifying circuit 



TRANSISTOR AMPLIFIER 

The function of a PNP or NPN transistor is 
very similar to that of a triode vacuum tube 
(although its operation is not so easily de- 
scribed). Fig. 14-27 shows a schematic transis- 
tor circuit that is analogous to the vacuum 
tube circuit shown in Fig. 14-26. In both 
cases, a small input signal controls a large 
output current. 



"/ ■. transistor 



/ 



input 
siqnal 



Fig. 14-27 



I'/jfo^wHs 



O 



Activities 



163 



Some inexpensive transistors can be bought at 
almost any radio supply store, and almost any 
PNP or NPN will do. Such stores also usually 
carry a variety of paper-back books that give 
simplified explanations of how transistors work 
and how you can use cheap components to 
build some simple electronic equipment. 

INSIDE A RADIO TUBE 

Receiving tubes, such as those found in radio 
and TV sets, contain many interesting parts 
that illustrates important physical and chemi- 
cal principles. 

Choose some discarded glass tubes at least 
two inches high. Your radio-TV serviceman 
will probably have some he can give you. Look 
up the tube numbers in a receiving tube 
manual and, if possible, find a triode. (The 
RCA Vacuum Tube Manual is available at 
most radio-TV supply stores for a couple of 
dollars.) WARNING: Do not attempt to open 
a TV picture tube!!! Even small TV picture 
tubes are very dangerous if they burst. 

Examine the tube and notice how the in- 
ternal parts are connected to the pins by wires 
located in the bottom of the tube. The glass- 
to-metal seal around the pins must maintain 
the high vacuum inside the tube. As the tube 
heats and cools, the pins and glass must ex- 
pand together. The pins are made of an iron- 
nickel alloy whose coefficient of expansion is 
close to that of the glass. The pins are coated 
with red copper oxide to bond the metal to 
the glass. 

The glass envelope was sealed to the glass 
base after the interior parts were assembled. 
Look at the base of the envelope and you can 
see where this seal was made. After assembly, 
air was drawn from the tube by a vacuum 
pump, and the tube was sealed. The sealing 
nib is at the top of miniature tubes and very 
old tubes, and is covered by the aligning pin 
at the bottom of octal-base tubes. 

The silvery material spread over part of 
the inside of the tube is called the getter. This 
coating (usually barium or aluminum) was 
vaporized inside the tube after sealing to 
absorb some more of the gas remaining in 
the envelope after it was pumped out. 



To open the tube, spread several layers of 
newspaper on a flat surface. Use goggles and 
gloves to prevent injury. With a triangular 
file, make a small scratch near the bottom. 
Wrap the tube with an old cloth, hold the tube 
with the scratch up on the table, and tap the 
tube with pliers or the file until it breaks. Un- 
wrap the broken tube carefully, and examine 
the pieces. The getter film will begin to change 
as soon as it is exposed to air. In a few minutes 
it will be a white, powderv' coating of barium 
or aluminum oxide. 

FrotiTjding from the bottom of the cage 
assembly are the wires to the pins. Identify 
the filament leads (there are 2 or 3) — very fine 
wires with a white ceramic coating. Cut the 
other wires with diagonal cutters, but leave 
the filament leads intact. Separate the cage 
from the base, and slide out the filament. 

The tube components in the cage are held 
in alignment with each other by the mica 
washers at the top and bottom of the cage. The 
mica also holds the cage in place inside the 
envelope. 



C^ 



cSg> 




l\ 



<S^ 



c^ 



CAGE ASSEMBLY 



l^;'?N BUTTON STEM 
''^' ASSEMBLY 



diagram of a 3-grid {"pentode") vacuum 



164 



Activities 



To separate the components, examine the 
ends that protrude through the mica washer, 
and decide what to do before the mica can be 
pulled off the ends. It may be necessary- to 
twist, cut. or bend these parts in order to dis- 
assemble the cage. When you have completed 
this operation, place the components on a 
clean piece of paper, and examine them one 
at a time. 

Mica was chosen as spacer material for 
its high strength, high electrical resistance, 
and the fact that it can withstand high tem- 
peratures. White mica consists of a complex 
compound of potassium, aluminum, silicon 
and oxygen in crystal form. Mica crystals have 
very weak bonds between the planes and so 
they can be split into thin sheets. Try it! 

The small metal cylinder with a white 
coating is the cathode. It is heated from inside 
by the filament. At operating temperature, 
electrons are "boiled off." 

The coating greatly increases the number 
of electrons emitted from the surface. When 
you wait for your radio or TV to warm up, you 
are waiting for the tube cathodes to warm up 
to an efficient emitting temperature. 

The ladder-like arrangement of very fine 
wire is called the grid. The electrons that were 
boiled off the cathode must pass through this 
grid. Therefore the current in the tube is very 
sensitive to the electric field around the grid. 

Small changes in the voltage of the grid 
can have a large effect on the flow of electrons 
through the tube. This controlling action is 
the basis for amplification and many other 
tube operations. 

The dark cvlinder that formed the outside 



of the cage is the plate. In an actual circuit, 
the plate is given a positive voltage relative 
to the cathode in order to attract the electrons 
emitted by the cathode. The electrons strike 
the plate and most give up their kinetic energy 
to the plate, which gets very hot. The plate is 
a dark color in order to help dissipate this heat 
energy. Often, the coating is a layer of carbon, 
which can be rubbed off with your finger. 

It is interesting to open different kinds of 
tubes and see how they differ. Some have more 
than one cage in the envelope, multiple grids, 
or beam-confining plates. The RCA Tube 
Manual is a good source for explanations of 
different tube types and their operation. 

AN ISOLATED NORTH MAGNETIC POLE? 

Magnets made of a rather soft rubber-like 
substance are available in some hardware 
stores. Typical magnets are flat pieces 20 mm 
X 25 mm and about 5 mm thick, with a mag- 
netic north pole on one 20 x 25 mm surface 
and south pole on the other. They may be cut 
with a sharp knife. 

Suppose you cut six of these so that you 
have six square pieces 20 mm on the edge. 
Then level the edges on the S side of each piece 
so that the pieces can be fitted together to 
form a hollow cube with all the N sides facing 
outward. The pieces repel each other strongly 
and may be either glued (with rubber cement) 
or tied together with thread. 

Do you now have an isolated north pole — 
that is. a north pole all over the outside (and 
south pole on the inside)? 

Is there a magnetic field directed outward 
from all surfaces of the cube? 



(Adapted from "Looking Inside a Vacuum Tube." Chem- 
istry, Sept. 1964.) 



(Adapted from The Physics Teacher. March 1966.) 



Chapter 



15 



Faraday and the Electrical Age 



ACTIVITIES 



FARADAY DISK DYNAMO 

You can easily build a disk dynamo similar to 
the one shown at the bottom of page 80 in 
Unit 4 Text. Cut an 8-inch-diameter disk of 
sheet copper. Drill a hole in the center of the 
disk, and put a bolt through the hole. Run a 
nut up tight against the disk so the disk wUl 
not slip on the bolt. Insert the bolt in a hand 
drill and clamp the drill in a ringstand so the 
disk passes through the region between the 
poles of a large magnet. Connect one wire of 
a 100-microamp dc meter to the metal part of 
the drill that doesn't turn. Tape the other wire 
to the magnet so it brushes lightly against the 
copper disk as the disk is spun between the 
magnet poles. 




Frantic cranking can create a 10-micro- 
amp current with the magnetron magnet 
shown above. If you use one of the metal yokes 
from the current balance, with three ceramic 
magnets on each side of the yoke, you may be 
able to get the needle to move from the zero 
position just noticeably. 



The braking effect of currents induced in 
the disk can also be noticed. Remove the meter, 
wires, and magnet. Have one person crank 
while another brings the magnet up to a posi- 
tion such that the disk is spinning between the 
magnet poles. Compare the effort needed to 
turn the disk with and without the magnet 
over the disk. 

If the disk will coast, compare the coast- 
ing times with and without the magnet in 
place. (If there is too much friction in the hand 
drUl for the disk to coast, loosen the nut and 
spin the disk by hand on the bolt.) 

GENERATOR JUMP ROPE 

With a piece of wire about twice the length of 
a room, and a sensitive galvanometer, you can 
generate an electric current using only the 
earth's magnetic field. Connect the ends of 
the wire to the meter. Pull the wire out into a 
long loop and twirl half the loop like a jump 
rope. As the wire cuts across the earth's mag- 
netic field, a voltage is generated. If you do 
not have a sensitive meter on hand, connect the 
input of one of the amplifiers, and connect the 
amplifier to a less sensitive meter. 

How does the current generated when the 
axis of rotation is along a north-south line com- 
pare with that current generated with the 
same motion along an east-west line? What 
does this tell you about the earth's magnetic 
field? Is there any effect if the people stand on 
two landings and hang the wire (whUe swing- 
ing it) down a stairwell? 




166 



Activities 



SIMPLE METERS AND MOTORS 



(from current 
balance kit) 



You can make workable current meters 
and motors from very simple parts: 
2 ceramic magnets! 
1 steel yoke i 

1 no. 7 cork J 

1 metal rod. about 2 mm in 

diameter and 12 cm long 

(a piece of bicycle spoke. 

coat hanger wire, or a 

large finishing nail 

will do) 

1 block of wood, about 10 cm x 5 cm x 1 cm 
About 3 yards of insulated no. 30 copper mag- 
net wire 

2 thumb tacks 
2 safety pins 

2 caipet tacks or small nailsl 
1 white card 4" x 5" > (for meter only) 

Stiff black paper, for pointerj 
Electrical insulating tape (for 
motor only) 

Meter 

To buUd a meter, follow the steps below pay- 
ing close attention to the diagrams. Push the 
rod through the cork. Make the rotating coil 
or armature by winding about 20 turns of 
wire around the cork, keeping the turns par- 
allel to the rod. Leave about a foot of wire at 
both ends (Fig. 15-1). 

Use nails or carpet tacks to fix two safety 








Fig. 15-2 



pins firmly to the ends of the wooden-base 
block (Fig. 15-2). 

Make a pointer out of the black paper, and 
push it onto the metal rod. Pin a piece of white 
card to one end of the base. Suspend the arma- 
ture between the two safety pins from the free 
ends of wire into two loose coUs. and attach 
them to the base with thumb tacks. Put the 
two ceramic magnets on the yoke (unlike poles 
facing), and place the yoke around the arma- 
ture (Fig. 15-3). Clean the insulation off the 
ends of the leads, and you are ready to connect 
your meter to a low-voltage dc source. 

Calibrate a scale in volts on the white card 
using a variety of known voltages from dry 
cells or from a low-voltage power supply, and 
your meter is complete. Minimize the parallax 
problem by having your pointer as close to 
the scale as possible. 




.eAcls to 
voltage sc^irct 



Fig. 15-1 



Fig. 15-3 



Activities 167 



Motor 

To make a motor, wind an armature as you 
did for the meter. Leave about 6 cm of wire 
at each end, from which you carefully scrape 
the insulation. Bend each into a loop and 
then twist into a tight pigtail. Tape the two 
pigtails along opposite sides of the metal 
rod (Fig. 15-4). 




Fig. 15-4 



Fix the two safety pins to the base as for 
the meter, and mount the coil between the 
safety pins. 

The leads into the motor are made from 
two pieces of wire attached to the baseboard 
with thumb tacks at points X (Fig. 15-5). 

Place the magnet yoke around the coil. 
The coil should spin freely (Fig. 15-6). 

Connect a 1.5-volt battery to the leads. 
Start the motor by spinning it with your 
finger. If it does not start, check the contacts 
between leads and the contact wires on the 
rod. You may not have removed all the enamel 
from the wires. Try pressing lightly at points 
A (Fig. 15-5) to improve the contact. Also check 
to see that the two contacts touch the armature 
wires at the same time. 

SIMPLE MOTOR-GENERATOR 
DEMONSTRATION 

With two fairly strong U-magnets and two 
coils, which you wind yourself, you can pre- 
pare a simple demonstration showing the prin- 
ciples of a motor and generator. Wind two flat 
coils of magnet wire 100 turns each. The card- 
board tube from a roll of paper towels makes 
a good form. Leave about i meter of wire free 
at each end of the coil. Tape the coil so it 
doesn't unwind when you remove it from the 
cardboard tube. 

Adapted from A Sourcebook for the Physical Sciences, 
Joseph and others; Harcourt, Brace and World, 1961, p. 529. 




Fig. 15-5 




Fig. 15-6 



Hang the coils from two supports as shown 
below so the coils pass over the poles of two 
U-magnets set on the table about one meter 
apart. Connect the coils together. Pull one coil 
to one side and release it. What happens to 
the other coil? Why? Does the same thing 
happen if the coils are not connected to each 
other? What if the magnets are reversed? 




168 



Activities 



Tr>- various other changes, such as turn- 
ing one of the magnets over while both coils 
are swinging, or starting with both coils at 
rest and then sliding one of the magnets back 
and forth. 

If you have a sensitive galvanometer, 
it is interesting to connect it between the 
two coils. 

PHYSICS COLLAGE 

Many of the words used in physics class enjoy 
wide usage in everyday language. Cut "physics 
words" out of magazines, newspapers, etc.. 
and make your own collage. You may wish to 
take on a more challenging art problem by 
tr>'ing to give a visual representation of a 
physical concept, such as speed, hght. or 
waves. The Reader 1 article, "Representation 
of Movement." may give you some ideas. 



BICYCLE GENERATOR 

The generator on a bicycle operates on the 
same basic principle as that described in the 
Text, but with a different, and extremely 
simple, design. Take apart such a generator 
and see if you can explain how it works. Note: 
You may not be able to reassemble it. 




fr\-:-U\iUm 




LAPIS POLARIS, MAGNES 

The etching (right) shows a philosopher in his 
study surrounded by the scientific equipment 
of his time. In the left foreground in a basin 
of water, a natural magnet or lodestone float- 
ing on a stick of wood orients itself north and 
south. Traders from the great Mediterranean 
port of Amalfi probably introduced the floating 
compass, having learned of it from Arab mari- 
ners. An Amalfi historian. Flavius Blondus, 
writing about 1450 a.d.. indicates the uncer- 
tain origin of the compass, but later historians 
in repeating this early reference warped it 
and gave credit for the discoven of the com- 
pass to Flavius. 

Can you identify the various devices lying 
around the study? When do you think the etch- 
ing was made? (If you have some background 
in art. you might consider whether your 
estimate on the basis of scientific clues is 
consistent with the style of the etching.) 



Activities 169 




LAPIS POLARIS, MAGNES. 
Lapis recltifit ifle Flauio ahditum ^oli Juum hunc amomn, at tpse nauita. 




Chapter 



16 



Electromagnetic Radiation 



EXPERIMENT 39 

WAVES AND COMMUNICATION 

Having studied many kinds and characteris- 
tics of waves in Units 3 and 4 of the Text, 
you are now in a position to see how they are 
used in communications. Here are some sug- 
gestions for investigations with equipment 
that you have probably already seen demon- 
strated. The following notes assume that you 
understand how to use the equipment. If you 
do not, then do not go on until you consult 
your teacher for instructions. Although differ- 
ent groups of students may use different 
equipment, all the investigations are related 
to the same phenomena — how we can com- 
municate with waves. 

A. Turntable Oscillators 

Turn on the oscillator with the pen attached 
to it. (See p. 310.) Turn on the chart recorder, 
but do not turn on the oscillator on which the 
recorder is mounted. The pen will trace out a 
sine curve as it goes back and forth over the 
moving paper. When you have recorded a few 
inches, turn off the oscillator and bring the pen 
to rest in the middle of the paper. Now turn on 
the second oscillator at the same rate that the 
first one was going. The pen will trace out a 
similar sine curve as the moving paper goes 
back and forth under it. The wavelengths of 
the two curves are probably very nearly, but 
not exactly, equal. 

Ql What do you predict will happen if you 
turn on both oscillators? Try it. Look care- 
fully at the pattern that is traced out with 
both oscillators on and compare it to the curves 



previously drawn by the two oscillators run- 
ning alone. 

Change the wavelength of one of the com- 
ponents slightly by putting weights on one of 
the platforms to slow it down a bit. Then make 
more traces from other pairs of sine curves. 
Each trace should consist, as in Fig. 16-1, of 
three parts: the sine curve from one oscillator; 
the sine curve from the other oscillator; and 
the composite curve from both oscillators. 
Q2 According to a mathematical analysis of 
the addition of sine waves, the wavelength of 
the envelope (k^ in Fig. 16-1) will increase as 
the wavelengths of the two components (A.,, A^) 
become more nearly equal. Do your results 
confirm this? 

Q3 If the two wavelengths X, and X2 were 
exactly equal, what pattern would you get 
when both turntables were turned on; that is, 
when the two sine curves were superposed? 
What else would the pattern depend on, as 
well as Xj and X.2? 

As the difference between X, and Xj gets 
smaller, X^ gets bigger. You can thus detect 
a very small difference in the two wavelengths 
by examining the resultant wave for changes 
in amplitude that take place over a relatively 
long distance. This method, called the method 
of beats, provides a sensitive way of compar- 
ing two oscillators, and of adjusting one until 
it has the same frequency as the other. 

This method of beats is also used for 
tuning musical instruments. If you play the 
same note on two instruments that are not 
quite in tune, you can hear the beats. And 
the more nearly in tune the two are, the lower 




Fig. 16-1 



viMWHI 



Experiment 39 



171 



the frequency of the beats. You might like to 
try this with two guitars or other musical 
instruments (or two strings on the same 
instrument). 

In radio communication, a signal can be 
transmitted by using it to modulate a "carrier" 
wave of much higher frequency. (See part E 
for further explanation of modulation.) A 
snapshot of the modulated wave looks similar 
to the beats you have been producing, but 
it results from one wave being used to con- 
trol the amplitude of the other, not from simply 
adding the waves together. 

B. Resonant Circuits 

You have probably seen a demonstration of how 
a signal can be transmitted from one tuned 
circuit to another. (If you have not seen the 
demonstration, you should set it up for your- 
self using the apparatus shown in Fig. 16.2.) 




Fig. 16-2 Two resonant circuit units. Each includes 
a wire coil and a variable capacitor. The unit on the 
right has an electric cell and ratchet to produce pulses 
of oscillation in its circuit. 

This setup is represented by the sche- 
matic drawing in Fig. 16-3. 



ostilla+oi^ 



Fig. 16-3 



QJ 



1. 



dicxk 






The two coils have to be quite close to each 
other for the receiver circuit to pick up the 
signal from the transmitter. 

Investigate the effect of changing the 
position of one of the coUs. Try turning one of 
them around, moving it farther away, etc. 
Q4 What happens when you put a sheet of 
metal, plastic, wood, cardboard, wet paper, 
or glass between the two coils? 



Q5 Why does an automobile always have an 
outside antenna, but a home radio does not? 
Q6 Why is it impossible to communicate 
with a submerged submarine by radio? 

You have probably learned that to transmit 
a signal from one circuit to another the two 
circuits must be tuned to the same frequency. 
To investigate the range of frequencies ob- 
tainable with your resonant circuit, connect 
an antenna (length of wire) to the resonant 
receiving circuit, in order to increase its sen- 
sitivity, and replace the speaker by an oscillo- 
scope (Fig. 16-4). Set the oscilloscope to 
"Internal Sync" and the sweep rate to about 
100 kilocycles/sec. 




Fig. 16-4 



Q7 Change the setting of the variable capa- 
citor ( =j^ ) and see how the trace on the 
oscilloscope changes. Which setting of the 
capacitor gives the highest frequency? which 
setting the lowest? By how much can you 
change the frequency by adjusting the ca- 
pacitor setting? 

When you tune a radio you are usually, 
in the same way, changing the setting of a 
variable capacitor to tune the circuit to a 
different frequency. 

The coil also plays a part in determining 
the resonant frequency of the circuit. If the 
coil has a different number of turns, a differ- 
ent setting of the capacitor would be needed 
to get the same frequency. 

C. Elementary Properties of Microwaves 

With a microwave generator, you can investi- 
gate some of the characteristics of short waves 
in the radio part of the electromagnetic spec- 
trum. In Experiment 30, "Introduction to 
Waves" and Experiment 31, "Sound," you 
explored the behavior of several different 
kinds of waves. These earlier experiments 



172 



Experiment 39 




contain a number of ideas that will help you 
show that the energy emitted by your micro- 
wave generator is in the form of waves. 

Refer to your notes on these experiments. 
Then, using the arrangements suggested 
there or ideas of your own, explore the trans- 
mission of microwaves through various 
materials as well as microwave reflection and 
refraction. Try to detect their diffraction 
around obstacles and through narrow openings 
in some material that is opaque to them. 
Finally, if you have two transmitters avail- 
able or a metal horn attachment with two 
openings, see if you can measure the wave- 
length using the interference method of 
Experiment 31. Compare your results with 
students doing the following experiment (D) 
on the interference of reflected microwaves. 

D. Interference of Reflected Microwaves 

With microwaves it is easy to demonstrate 
interference between direct radiation from a 
source and radiation reflected from a flat 
surface, such as a metal sheet. At points where 



the direct and reflected waves arrive in phase, 
there will be maxima and at points where 
they arrive 2^-cycle out of phase, there will 
be minima. The maxima and minima are 
readily found by moving the detector along 
a line perpendicular to the reflector. (Fig. 16-5.) 
Q8 Can you state a rule with which you 
could predict the positions of maxima and 
minima? 

By moving the detector back a ways and 
scanning again, etc., you can sketch out lines 
of maxima and minima. 

Q9 How is the interference pattern similar 
to what you have observed for two-source 
radiation? 

reflector 






: ^ 



\ 



\ 



1 . ri«t»Tt. 



Fig. 16-5 



Fine 



V 



Experiment 39 



173 




Standing microwaves will be set up if the 
reflector is placed exactly perpendicular to 
the source. (As with other standing waves, 
the nodes are j wavelength apart.) Locate 
several nodes by moving the detector along a 
line between the source and reflector, and from 
the node separation calculate the wavelength 
of the microwaves. 

QIO What is the wavelength of your micro- 
waves? 

Qll Microwaves, like light, propagate at 
3 X 10 m/sec. What is the frequency of your 
microwaves? Check your answer against the 
chart of the electromagnetic spectrum given 
on page 113 of Tex^ Chapter 16. 

The interference between direct and 
reflected radio waves has important practical 
consequences. There are layers of partly 
ionized (and therefore electrically conducting) 
air, collectively called the ionosphere, that 
surrounds the earth roughly 30 to 300 kilo- 
meters above its surface. One of the layers at 
about 300 km is a good reflector for radio 
waves, so it is used to bounce radio messages 
to points that, because of the curvature of the 
earth, are too far away to be reached in a 
straight line. 

If the transmitting tower is 100 meters 
high, then, as shown roughly in Fig. 16-6, 
point A -the farthest point that the signal can 
reach directly in flat country -is 35 kilometers 
(about 20 miles) away. But by reflection from 
the ionosphere, a signal can reach around the 
corner to B and bevond. 






\ 



\ 



transmlffei 



Fig. 16-6 




Sometimes both a direct and a reflected 
signal will arrive at the same place and in- 
terference occurs; if the two are out of phase 
and have identical amplitudes, the receiver 
will pick up nothing. Such destructive inter- 
ference is responsible for radio fading. It is 
complicated by the fact that the height of the 
ionosphere and the intensity of reflection from 
it vary during the day with the amount of 
sunlight. 

The setup in Fig. 16-7 is a model of this 
situation. Move the reflector (the "ionosphere") 
back and forth. What happens to the signal 
strength? 



rriove reflector 
hack. f^6 forth 




Fig. 16-7 



There can also be multiple reflections - 
the radiation can bounce back and forth be- 



174 



Experiment 39 



tween earth and ionosphere several times on 
its way from, say. New York to Calcutta, 
India. Perhaps you can simulate this situation 
too with your microwave equipment. 

£. Signals and Microwaves 

Thus far you have been learning about the 
behavior of microwaves of a single frequency 
and constant amplitude. A signal can be 
added to these waves by changing their ampli- 
tude at the transmitter. The most obvious way 
would be just to turn them on and off as rep- 
resented in Fig. 16-8. Code messages can be 
transmitted in this primitive fashion. But 




Fig. 16-8 

the wave amplitude can be varied in a more 
elaborate way to carry music or voice signals. 
For example, a 1000 cycle/sec sine wave fed 
into part of the microwave transmitter will 
cause the amplitude of the microwave to 
vary smoothly at 1000 cyc/sec. 

Controlling the amplitude of the trans- 
mitted wave like this is called amplitude 
modulation; Fig. 16-9A represents the un- 
modulated microwave. Fig. 16-9B represents 
a modulating signal, and Fig. 16-9C the modu- 
lated microwave. The Damon microwave 
oscillator has an input for a modulating 
signal. You can modulate the microwave 
output with a variety of signals, for example, 
with an audio-frequency oscillator or with a 
microphone and amplifier. 

The microwave detector probe is a one-way 
device — it passes current in only one direction. 
If the microwave reaching the probe is repre- 
sented in C, then the electric signal from the 
probe will be like in D. 

You can see this on the oscilloscope by 
connecting it to the microwave probe (through 
an amplifier if necessary). 

The detected modulated signal from the 
probe can be turned into sound by connecting 
an amplifier and loudspeaker to the probe. The 





AjW 



A k 



i(W-AJ\Jlji 



1^ 



llk,.„^/lA]Ln..,..JlillW 






Fig. 16-9 

speaker will not be able to respond to the 10^ 
individual pulses per second of the "carrier" 
wave, but only to their averaged effect, repre- 
sented by the dotted line in E. Consequently, 
the sound output of the speaker will cor- 
respond very nearly to the modulating signal. 
Ql 2 Why must the carrier frequency be much 
greater than the signal frequency? 
Q13 Why is a higher frequency needed to 
transmit television signals than radio signals? 
(The highest frequency necessary to convey 
radio sound information is about 12,000 cycles 
per second. The electron beam in a television 
tube completes one picture of 525 lines in 1/30 
of a second, and the intensity of the beam 
should be able to vary several hundred times 
during a single line scan.) 



ACTIVITIES 



MICROWAVE TRANSMISSION SYSTEMS 

Microwaves of about 6-cm wavelength are 
used to transmit telephone conversations over 
long distances. Because microwave radiation 
has a limited range (they are not reflected well 
by the ionosphere), a series of relay stations 
have been erected about 30 miles apart across 
the country. At each station the signal is de- 
tected and amplified before being retrans- 
mitted to the next one. If you have several 
microwave generators that can be amplitude 
modulated, see if you can put together a 
demonstration of how this system works. You 
will need an audio-frequency oscillator (or 
microphone), amplifier, microwave generator 
and power supply, detector, another amplifier, 
and a loudspeaker, another microwave gen- 
erator, another detector, a third amplifier, 
and a loudspeaker. 

SCIENCE AND THE ARTIST-THE STORY 
BEHIND A NEW SCIENCE STAMP 

The sciences and the arts are sometimes 
thought of as two distinct cultures with a 
yawning gulf between them. Perhaps to help 
bridge that gulf, the Post Office Department 
held an unprecedented competition among 
five artists for the design of a postage stamp 
honoring the sciences. 



U.S. POSTAGE 



THE SCIENCES 







The winning design by Antonio Frasconi. The stamp 
was printed in light blue and black. 

The winning stamp, issued on October 
14, 1963, commemorates the 100th anniver- 
sary of the National Academy of Sciences 
(NAS). This agency was estabhshed during the 
Civil War with the objective that it "shall, 
whenever called upon by any department of 



government, investigate, experiment, and 
report upon any subject of science or of art." 

To celebrate the NAS anniversary, the late 
President John F. Kennedy addressed the 
members of the academy and their distin- 
guished guests from foreign scientific soci- 
eties. After emphasizing present public 
recognition of the importance of pure science, 
the President pointed out how the discoveries 
of science are forcing the nations to cooperate: 

"Every time you scientists make a major in- 
vention, we politicians have to invent a new institu- 
tion to cope with it-and almost invariably these 
days it must be an international institution." 

As examples of these international insti- 
tutions, he cited the International Atomic 
Energy Agency, the treaty opening Antarctica 
to world scientific research, and the Inter- 
governmental Oceanographic Commission. 

In the scientific sessions marking the 
NAS anniversan,. the latest views of man and 
matter and their evolution were discussed, as 
well as the problem of financing future re- 
searches -the proper allocation of limited 
funds to space research and medicine, the 
biological and the physical sciences. 

The stamp competition was initiated by 
the National Gallery of Art, Washington, D.C. 
A jury of three distinguished art specialists 
invited five American artists to submit designs. 
The artists were chosen for their "demon- 
strated appropriateness to work on the theme 
of science." They were Josef Albers. Herbert 
Bayer, Antonio Frasconi, Buckminster Fuller, 
and Bradbury Thompson. 

Albers and Bayer both taught at the 
Bauhaus (Germany), a pioneering design 
center that welded modern industrial know- 
how to the insights of modern art. (The Bau- 
haus is probably best known for its develop- 
ment of tubular steel furniture.) Albers has 
recently published what promises to be the 
definitive work on color-Interaction of Color 
(Yale University Press). Bayer is an architect 
as well as an artist; he has designed several 
of the buildings for the Institute of Humanistic 
Studies in Aspen, Colorado. Buckminster 
Fuller, engineer, designer, writer, and in- 



176 Activities 



THE SCIENCES 




UNITED STATES POSTAGE 



Alters 




s \ ', 




Bayer 




SCIENCE 




I ■ S I>OSTAGF. 

5 CENTS 



Fuller 



S( 



ego 

U.S. POSTAGE 

5 CENTS 



THE S( lENCKJ 




5 






Frasconi 



Thompson 



Activities 



177 



ventor, is the creator of the geodesic dome, 
the Dymaxion three-wheeled car, and Dy- 
maxion map projection. Frasconi, bom in 
Uruguay, is particularly known for his wood- 
cuts; he won the 1960 Grand Prix Award at 
the Venice Film Festival for his film, The 
Neighboring Shore. Bradbury Thompson is 
the designer for a number of publications 
including Art News. 

Ten of the designs submitted by the artists 
are shown on the opposite page. The Citizen's 
Stamp Advisory Committee chose four of the 
designs from which former Postmaster Gen- 
eral J. Edward Day chose the winner. The 
winning design by Frasconi, depicts a stylized 
representation of the world, above which 
is spread the sky luminescent with stars. 

Which design do you feel most effectively 
represents the spirit and character of science, 
and why? If you are not enthusiastic about 
any of the stamps, design your own. 

BELL TELEPHONE SCIENCE KITS 

Bell Telephone Laboratories have produced 
several kits related to topics in Unit 4. Your 
local Bell Telephone office may be able to pro- 
vide a limited number of them for you free. 
A brief description follows. 

"Crystals and Light" includes materials 
to assemble a simple microscope, polarizing 



filters, sample crystals, a book of experiments, 
and a more comprehensive book about crystals. 

"Energy from the Sun" contains raw 
materials and instructions for making your 
own solar cell, experiments for determining 
solar-cell characteristics, and details for 
building a light-powered pendulum, a light- 
commutated motor, and a radio receiver. 

"Speech Synthesis" enables you to as- 
semble a simple battery-powered circuit to 
artificially produce the vowel sounds. A booklet 
describes similarities between the circuit and 
human voice production, and discusses early 
attempts to create artificial voice machines. 

"From Sun to Sound" contains a ready- 
made solar cell, a booklet, and materials for 
building a solar-powered radio. 

Good Reading 

Several good paperbacks in the science Study 
Series (Anchor Books, Doubleday and Co.) 
are appropriate for Unit 4, including The 
Physics of Television, by Donald G. Fink and 
David M. Lutyens; Waves and Messages by 
John R. Pierce; Quantum Electronics by John 
R. Pierce; Electrons and Waves by John R. 
Pierce; Computers and the Human Mind, 
by Donald G. Fink. See also "Telephone 
Switching," Scientific American, July, 1962, 
and the Project Physics Reader 4. 




FILM LOOP 



FILM LOOP 45: STANDING 
ELECTROMAGNETIC WAVES 

Standing waves are not confined to mechani- 
cal waves in strings or in gas. It is only neces- 
sary to reflect the wave at the proper distance 
from a source so that two oppositely moving 
waves superpose in just the right way. In this 
film, standing electromagnetic waves are 
generated by a radio transmitter. 

The transmitter produces electromagnetic 
radiation at a frequency of 435 x 10" cycles/sec. 
Since all electromagnetic waves travel at the 
speed of light, the wavelength is X = c// = 
0.69 m. The output of the transmitter oscil- 
lator (Fig. 16-10) passes through a power- 
indicating meter, then to an antenna of two 
rods each j X long. 




oscillator PONer Ttaf^sf^iftim i^eceivf/ve 

^35)1 10*' //ez'i?/- DiPoue DiPoce 

cvcies/sec. A/^re/v/va ANteNAjot 

Fig. 16-10 

The receiving antenna (Fig. 16-11) is also 
i A. long. The receiver is a flashlight bulb con- 
nected between two stiff wires each i X long. 
If the electric field of the incoming wave is 
parallel to the receiving antenna, the force 
on the electrons in the wire drives them back 
and forth through the bulb. The brightness of 
the bulb indicates the intensity of the electro- 
magnetic radiation at the antenna. A rec- 
tangular aluminum cavity, open toward the 
camera, confines the waves to provide suffi- 
cient intensity. 

Initial scenes show how the intensity 
depends on the distance of the receiving 
antenna from the transmitting antenna. The 
radiated power is about 20 watts. Does the 
received intensity decrease as the distance 
increases? The radiation has vertical polariza- 
tion, so the response falls to zero when the 




Fig. 16-11 

receiving antenna is rotated to the horizontal 
position. 

Standing waves are set up when a metal 
reflector is placed at the right end of the 
cavity. The reflector can't be placed just any- 
where; it must be at a node. The distance from 
source to reflector must be an integral number 
of half-wavelengths plus j of a wavelength. 
The cavity length must be "tuned" to the 
wavelength. Nodes and antinodes are identi- 
fied by moving a receiving antenna back and 
forth. Then a row of vertical receiving an- 
tennas is placed in the cavity, and the nodes 
and antinodes are shown by the pattern of 
brilliance of the lamp bulbs. How many nodes 
and antinodes can be seen in each trial? 

Standing waves of different types can all 
have the same wavelength. In each case a 
source is required (tuning fork, loudspeaker, 
or dipole antenna). A reflector is also necessary 
(support for string, wooden piston, or sheet 
aluminum mirror). If the frequencies are 72 
vib/sec for the string, 505 vib sec for the gas, 
and 435 x 10* vib/sec for the electromagnetic 
waves and all have the same wavelength, 
what can you conclude about the speeds of 
these three kinds of waves? Discuss the 
similarities and diflFerences between the 
three cases. What can you say about the 
"medium" in which the electromagnetic 
waves travel? 



Sidney Rosen, University of Illinois, Urbana 
John J. Rosenbaum, Livermore High School 

Calif. 
William Rosenfeld, Smith College, Northampton, 

Mass. 
Arthur Rothman, State University of New York, 

Buffalo 
Daniel Rufolo, Clairemont High School, San 

Diego, Calif. 

Bemhard A. Sachs, Brooklyn Technical High 

School, N.Y. 
Morton L. Schagrin, Denison University, Granville 

Ohio 

Rudolph Schiller, Valley High School, Las Vegas, 

Nev. 
Myron O. Schneiderwent, Interlochen Arts 

Academy, Mich. 
Guenter Schwarz, Florida State University, 

Tallahassee 
Sherman D. Sheppard, Oak Ridge High School, 

Tenn. 
William E. Shortall, Lansdowne High School, 

Baltimore, Md. 
Devon Showley, Cypress Junior College, Calif. 
William Shurcliff. Cambridge Electron 

Accelerator, Mass. 
Katherine J. Sopka, Harvard University 
George I. Squibb, Harvard University 
Sister M. Suzanne Kelley, O.S.B., Monte Casino 

High School, Tulsa, Okla. 
Sister Mary Christine Martens, Convent of the 

Visitation, St. Paul, Minn. 
Sister M. Helen St. Paul, O.S.F., The Catholic 

High School of Baltimore, Md. 



Staff and Consultants 

M. Daniel Smith, Earlham College, Richmond 

Ind. 
Sam Standring, Santa Fe High School, Santa Fe 

Springs, Calif. 
Albert B. Stewart, Antioch College, YeUow 

Springs, Ohio 
Robert T. SuUivan, Burnt Hills-Ballston Lake 

Central School, N.Y. 
Loyd S. Swenson, University of Houston, Texas 
Thomas E. Thorpe, West High School, Phoenix, 

Ariz. 
June Goodfield Toulmin, Nuffield Foundation, 

London, England 
Stephen E. Toulmin, Nuffield Foundation, London, 

England 
Emily H. Van Zee, Harvard University 
Ann Venable, Arthur D. Little, Inc., Cambridge, 

Mass. 
W. O. Viens, Nova High School, Fort Lauderdale, 

Fla. 
Herbert J. Walberg, Harvard University 
Eleanor Webster, Wellesley College, Mass. 
Wayne W. Welch, University of Wisconsin, 

Madison 
Richard Weller, Harvard University 
Arthur Western, Melbourne High School, Fla. 
Haven Whiteside, University of Maryland, College 

Park 
R. Brady Williamson, Massachusetts Institute of 

Technology, Cambridge 
Stephen S. Winter, State University of New York 
Buffalo 



179 



INDEX/TEXT SECTION 



Academy of Sciences, 9, 10 
Acceleration, 58 
Accelerators, electron, 56, 57 

particle, 57 
Aerobee rocket, 118-119 
Air pressure, 44 
Alice in Wonderland, (see 

Cheshire cat) 
Alternating current, 83, 92, 93 
Alternating current generator, 

82-84 
Amber, 32, 35 
Ampere, Andre-Marie, 39, 62, 63, 

76, 77 
Ampere, unit, 63 

Amplitude modulation CAM), 116 
Angle of incidence, 11 
Angstrom, Anders Jonas, 20 
Angstrom unit (A), 20 
Annals of Philosophy, 76 
Appliances, electric, 98 
Arc lamp, 87 
Aurora, 68 

Bacon, Francis, 14 
Balanced forces, 50 
Bar magnet, 62 
Bartholinus, Erasmus, 22 
Battery, 54, 55, 56, 93 
Blackmore, Richard, 5 
Bently, Richard, 2 
Biot, 76 
Browne, Sir Thomas, 35 

Calcite (Iceland spar), 22 
Cambridge Philosophical Society, 

104 
Camera obscura, 8 
Capacitors, 52 
Carnot, Sadi, 85 
Charge, 36, 37, 38-39, 47, 60, 66 

conservation of, 52 

electrical, 35 

moving, 53 

speed of, 67 

unit of, 39 
Cheshire cat, grin, 125 
Circuit 

parallel, 89 

series, 89 
Coil, induction. 111, 112 

of wire, 62, 64, 66, 91 
Collisions, 59 
Color, 15, 17-21 

apparent, 18 

properties of, 18-20 

spectrum of, 17 



Commutator, 83, 90 
Communications, electrical, 99 
Compasses, 61 
Conductor, 40, 53, 105 

metaUic, 58 
Conservation, of charge, 52 
Corpuscular model, 6 
Coulomb, Charles, 37 

law, 39, 41, 46, 58, 66 

Theory of Simple Machines, 38 

unit, 39 
Current, 54, 58, 63, 91 

alternating, (see Alternating 
current) 

direct, (see Direct current) 

displacement, 105 

electrical, 53 

da Vinci, Leonardo, 6, 8, 15 
Davy, Sir Humphrey, 78, 87 
De Magnete (Gilbert), 32-33 
Diffraction 

image, 16 

light, 6, 13-15, 16 

pattern, 14, 16 
Direct current (DC), 83, 90-91 
Dispersion, of light, 6 
Displacement current, 105 
Double refraction, 22 
Double-slit experiment (Young), 

13 
Dynamo, 81, 84, 85 

Edinburgh Review, 14 

Edison, Thomas Alva, 87, 88, 89, 

92 
Edison Electric Light Company, 90 
Einstein, Albert, 25, 123-124 
Electric attraction, 34—35 

charge, 35, 54, 60, 66, 67 

currents, 53, 58, 60, 62, 66, 83, 
84,91, 105 

field, 46, 47, 49, 80, 105, 106, 107 

force, 66 

generator, 80, 87 

light bulb, 86 

motor, 66, 76, 84-86 

potential difference, 58, 59 

power, 59, 91 

repulsion, 35, 41 

work, 55—56 
Electric energy, 81 
Electricity, 34 

appliances, 98 

commercial distribution of 
power, 96-97 



communications, 99 

and machines, 51 

and magnetism, 35—36, 60, 62 

major U.S. transmission lines, 
96-97 

potential difference, 55-57 

power age, 84 

and society, 94-95, 98-99 
Electrocution, 92 
Electromagnet, 64—65 
Electromagnetic induction, 77-81, 

85, 107 
Electromagnetic radiation, 113, 

115 
Electromagnetic rotator, 76 
Electromagnetic spectrum, 114— 

116 
Electromagnetic waves, propaga- 
tion of , 107, 108 

speed of , 112, 114 
Electromagnetism, 2, 3, 76, 104— 

107 
Electron, 56, 57, 58 
Electron accelerators, 56, 57 
Electron gun, 56, 66 
Electron volt (ev), 56 
Electrostatics, 2, 35 

experiment in, 53, 77 

induction, 41, 77 
Energy, 55 

electrical, 81 

electric potential, 55—57 

kinetic, 56 

light, 5 

magnetic, 81 
Engine, steam, 75 
Ether, 2, 24, 121, 122-123 
Explorer I, 68 

Faraday, Michael, 2, 3, 34, 76, 77, 
78,79,80,84,85,103, 104, 
107 
Federal Communications Commis- 
sion (FCC), 116 
Feynman, Richard, 126 
Field,2,3,42, 45, 80 

electric, 46, 105, 106, 107 

gravitational, 45 

magnetic 34, 42, 60, 66-68, 81- 

84, 105, 106, 107 
pressure and velocity, 44 
scalar, 45 
vector, 45, 46 
Filament, 87, 89 
Fizeau, 110 
Fizeau-Foucault experiments, 13 



180 



Fluids, 36 

negative, 36 

positive, 36 
Force, 66 

attractive, 11, 12 

balanced, 50 

direction of, 67 

electric lines of, 104 

gravitational, 37, 50 

lawof, 37, 63 

lines of, 104-105 

magnetic lines of, 104 

repulsive, 11 

zero, 37 
Foucault-Fizeau experiments, 13 
Franklin, Benjamin, 36, 37, 52 
French Academy of Sciences, 63 
French Revolution, 37, 62 
Frequency modulation (FM), 116 
Frequency unit, 114 
Fresnel, Augustin, 14, 15, 22, 24 
Frisius, Gemma, 8 

Galileo, 9, 46, 124 
Gamma rays, 120 
Gauss, unit, 63 

Generator, alternating-current, 
82-84 

electric, 80, 87 

water driven, 86 
Gilbert, William, 32-33. 34, 42 
Glover, Richard, 24 
Goethe, Johann Wolfgang von, 20 
Gravitation, law of, 37, 39 
Gravitational field, 46 
Gravitational attraction, 46 
Gravitational force, 37, 45, 50 
Guericke, Otto von, 51 

Henry, Joseph, 65, 77, 84, 92 

Herapathite, 22 

Hertz, Heinrich, 91, 92, 111, 112, 

114 
Hilac, 31 

Hooke, Robert, 19, 21 
Hull, 114 

Huygens, Christiaan, 6, 10, 12, 21 
Hydroelectric power, 93, 94 
Hypothesis, 6 

Iceland spar (calcite), 22 
Induction coil. 111, 112 
Industrialization, 98 
Infrared radiation, 117 
Insect eyes, and polarization, 23 
Insulating material, 105 
Insulators, 53 



Interaction, region of, 42 
Interference, light, 6, 13-15 
International Electrical Exhibition 

93 
International Telecommunications 

Union (ITU), 116 
Inverse-square law, 37 

Joule, 59 
joule, unit, 55 
Jupiter, satellites of, 9 

Kelvin scale, 2 
Kilowatt-hour, 63 
Kinetic energy, 56 
Kohlrausch, 110 

Land, Edwin H., 22 

Lebedev, 114 

Leyden jar, 52, 54 

Light, diffraction of, 6, 13-15, 16 

dispersion of, 6 

interference, 6, 13-15 

and magnetism, 104 

particle model of, 12 

polarization, 6, 21-23 

propagation of, 6, 8-10 

properties of, 5-6 

reflection of , 6, 11-13 

refraction of, 6, 11-13 

scattering of, 6 

speed of, 9, 10, 110 

ultraviolet, 117 

unpolarized, 22 

violet, 118-119 

visible, 117 

wavelengths of, 20 

wave model of, 6 

wave-theory of, 1 
Light bulb, 86-87, 89-90 
Light energy, 5 
Lightning, 41 
Lightning rod, 36 
Light ray, 8, 9, 10-15, 17-19 
Light waves, 20, 21-23 

polarized, 22 
Lines of force, 104-105 
Lodestone, 32, 34, 42 
Lucretius, 32 
Luminiferous ether, {see Ether) 

Machines, electrical, 51 
Magnet, 60, 62 

bar, 62 
Magnetic energy, 81 
Magnetic field, 34, 42, 60, 66-68, 
81-84, 105, 106, 107 



central, 60 

circular, 60, 76 

perpendicular, 60 
Magnetism, 32-34 

and hght, 103-104 
Maxwell, James Clark, 2, 3, 62, 
104, 105, 108, 111, 121, 122, 
123 

systhesis of electromagnetism 
and optics, 110 
Metallic conductor, 58 
Michelson, Albert, 123 
Millikan, Robert A., 50, 56 
"MKSA" system, 39 
Morely, Edward, 123 
Motor, electric, 66, 76, 84-86 
Model, 6 

light, 1 

particle, 11, 12-13 

wave, 12 
Musschenbroek, Pieter van, 51, 52 

Napoleon, 54 

Nature-philosophers, 19, 60, 103 
Newton, Isaac, 1, 2, 6, 12, 13, 15, 
17,18,21,22,24,37 

law of gravitation 37, 39 

Opticks, 19 

Principia, 19 

reactions to his theory of color, 
19 

theory of color, 17-19 

third law, 107 
Niagara Falls power plant, 90-94 
Nichols, 114 

Oersted, Hans Christian, 60, 61, 62, 

63, 66, 76, 77 
Ohm's Law, 58 
Opticks (Newton), 12, 19 
Orbiting Solar Observatory, 118- 

119 
Oscilloscope, 57 

Parallel circuit, 89 
Particle accelerators, 57 
Particle model, 11, 12-13, 15 
Philosophical Transactions, 17 
Photoelectric effect, 112 
Photosynthesis, 5 
Pixii, Hippolyte, 83 
Poisson, Simon, 15 
Polarization 

and insect eyes, 23 

oflight, 6, 21,23 

sheet, 22-23 
Polaroid, 22 



181 



Polymeric molecules, 22 
Population, decentralization of, 98 
Potential difference, 58, 59 
Power, 59, 91 
Priestley, Joseph, 37 
Primary, coil, 91 
Principia (Newton), 19, 37 
Prism, 17 

Propagation, of electromagnetic 
waves, 108 
oflight, 6, 8-10 

Radar, 116-117 
Radiant heat, 117 
Radiation, electromagnetic, 113, 
115 

infrared, 117 
Radio, 115-116 
Radio telescope, 102 
Radio waves, 115-116 
Rays, gamma, 120 

of light, 8, 9 
Reflection, light, 11-13 
Refraction, double, 22 

oflight, 11-13,22-23 
Region, of interaction, 42 
Relativity, principle of, 124 
Resistance, 58, 89 
Resistors, 58 

Roosevelt, Franklin D., 95 
Romantic movement, 19 
Romer, Ole, 9, 10 
Royal Institution (London), 78, 

103 
Royal Observatory, 9 
Royal Society of Edinburgh, 122 
Royal Society of London, 17, 54 



Satellite, communications relay, 
116 

of Jupiter, 9 
Savart, 76 
Scalar field, 45 
Scattering, of light, 6 
Schelling, Friedrich, 19, 61 
Secondary coU, 91 
Series circuit, 89 
Seurat, Georges, 25 
Sky, color of, 20-21 
Spark, 53 
Spectrum of colors, 17 

electromagnetic, 114-116 
Speed, of Hght, 70 
Sprengel, Hermann, 87 
Steam engine, 75, 91 
Sturgeon, William, 65 

Telescope, 

radio, 102, 118-119 
Television, 116-117 

tube, 40 
Tennessee Valley Authority, 86, 95 
Terrella, 34 
The Theory of Simple Machines 

(Coulomb), 38 
Thomson, James, 19 
Thomson, William (Lord Kelvin), 

2,3 
Torsion balance, 37, 38 
Transformer, 91, 92 
Turbine steam, 91 

Ultraviolet light, 117 
Undulation, 14 



University of Cambridge England, 

122 
Unpolarized light, 22 

Vacuum-tube circuit, 108 
Van Allen, James A., 68 
Van Allen radiation belt, 68 
Vector field, 45, 46 
Velocity, magnitude of, 66 

wind, 44 
Vienna Exhibition, 84 
Violet light, 118 
Visible light, 117 
Volt, 56 
Volta, Alessandro, 54, 75 

battery, 54 
Voltage, 55, 56, 57, 59 
Voltaic cell, 54, 56 
Voltaic pile, 54 

Watt, 63 

Waves, electromagnetic, 107-108 

radio, 115-116 
Wavelength, and scattering, 20 
Wave model, 6, 12 
Weather maps, 44 
Weber, 110 

Westinghouse, George, 92 
Wheatstone, Sir Charles, 103 
White light, 18 
Work, 55-56, 59 

Xrays, 117, 120 

X-ray telescope, 118-119 

Young, Thomas, 13, 14-15, 20, 21, 
22,24 



182 



INDEX/HANDBOOK SECTION 



Activities : 

Additional activities using the electron beam 
tube, 160-164 

Bell Telephone science kits, 177 

Bicycle generator, 168 

Color, 139-140 

Detecting electric fields, 158 

Faraday disk dynamo, 165 

Generator jump rope, 165 

Handkerchief diffraction grating, 138 

Isolated North Pole, 164 

Lapis Polaris Magnes, 168-169 

Make an ice lens, 141 

Measuring magnetic field intensity, 158-159 

Microwave transmission systems, 175 

More perpetual motion machines, 159-160 

Photographic activities, 139 

Photographing diffraction patterns, 138 

Physics collage, 168 

Poisson's spot, 139 

Polarized hght, 140-141 

Science and the Artist— The story behind a 
new science stamp, 175 

Simple meters and motors, 167 

Simple motor-generator demonstration, 
167-168 

Thin film interference, 138 
Adventures of Captain Hatteras, The (Jules 

Verne), 141 
Amplitude modulation, 174 
Angle(s), of incidence and refraction, 134-135 
Angrist, Stanley W., "Perpetual Motion 

Machines," 159 
Antarctica, opening to world scientific research 

175 
Armature, construction of, 166 

Balance, construction and use of, 144-145 

current, 147, 152-154 
Balanced loop, current balance, 147, 149, 152-153 
Battery, eleven cent, construction of (activity) 

158 
Bauhaus design center, 175 

Beats, method of comparing frequencies, 170-171 
Bell Telephone Science Kits (activity), 177 
Bicycle generator (activity), 168 
Bondus, Flavins, and origin of compass, 168 
Bradij, Matthew (James D. Horan), 139 

Cathode, radio tube, 163-164 
"Cathode rays," nature of, 157 
Charge(s), electric (see also Electric charge), 
free, 155 
speed of, 157 
Charged bodies, electric force between, 144-146 
Charged pith ball (activity), 158 
Circular polarizer, construction of, 141 
Collage, physics (activity), 168 



Color (s), refraction of, 135 

physiological and psychological aspects 
(activity), 139-140 
Communication, and waves (experiment), 

170-174 
"Compass," electric, construction of (activity) 
158 
floating, 168-169 
origin of, 168-169 
Computers and the Human Mind (Donald R. 

Fink), 177 
Coulomb's Law, 144-146 
"Crystals and Light," science kit, 177 
Current(s), electric, interaction with earth, 
153-154 
forces on (experiment), 147-151 
and magnet, force between, 152-153 
magnets and forces (experiment), 152-154 
Current balance, 147-154 
adjustment of, 147-149 
connections, 148 

Diffraction pattern, photographing of, 138 
Diode and triode characteristics of electronic 

vacuum tubes (activity), 161-162 
Disk dynamo, construction of (activity), 165 
Dispersion of colors in refraction, 135 
Dynamo, disk, construction of (activity), 165 

Earth, interaction with electric current, 153-154 
magnetic field and generating electric current 
165 
Electric "compass," construction of (activity) 

158 
Electric charges, 142-143, 155, 157 
Electric currents, force between, 147-151 
Electric field, 155 

and deflection of electron beam, 156 
detection of (activity), 158 
Electric and magnetic effects, balancing of, 157 
Electric force, measurement of, 144-146 
Electric forces I (experiment), 142-143 
Electric forces II— Coulomb's Law (experiment) 

144-146 
Electromagnetic waves, standing, 178 
Electron beam, 155 
deflection of , 156 
focusing of, 160-161 
reflecting of (activity), 161 
Electron beam tube (activity), 160-164 
(experiment), 155-157 
construction and operation of, 155-156, 

160-161 
and vacuum tube characteristics (activity), 
161-162 
Electronic vacuum tubes, see vacuum tubes 
Electrons and Waves (John R. Pierce), 177 



183 



Eleven cent battery, construction of (activity), 
158 

"Energ>' from the Sun," science kit, 177 

Experiments : 

Currents, magnets and forces, 152-154 
Electric forces I, 142-143 
Electric forces II — Coulomb's Law, 144-146 
Electron beam tube, 155—157 
Forces on currents, 147-151 
Refraction of a light beam, 134—135 
Waves and communication, 170—174 
Young's Experiment — The wavelength of light, 
136-137 



Land effect (activity), 140 

Land two-color demonstrations, 140 

Lapis Polaris Magnes (activity), 168-169 

Latent Image (Beaumont Newhall), 139 

Life Magazine (December 23, 1966) photography 

issue, 139 
Light, interference pattern of, 136-137 

frequencies of, 137 

polarized, 140-141 

speed in air, 137 

wavelength of, 136-137 

see also color 
Light beam, refraction of (experiment), 134-135 



Faraday disk dynamo, construction of (activity), 
165 

Film loop : 

Standing electromagnetic waves, 178 

Flatness of surface, determination of, 138 

Floating compass, 168-169 

Force, electric, between current and magnet, 
149, 152-153 
on currents (experiment), 147—151 
and distance between wires, 149-150 
and variation in wire length, 150-151 

Foundations of Modem Physical Science (Holton 
and Roller), 158 

Frasconi, Antonio, The Neighboring Shore, 177 
and science stamp competition, 175 

Free charges, electric, 155 

Frequency range, 171 

"From Sun to Sound," science kit, 177 

Gauss, 159 

Generator jump rope (activity), 165 

Getter, radio tube, 163 

Grid, radio tube, 163-164 

Handkerchief diffraction grating (activity), 138 

Helix, 161 

History of Science Cases for High Schools 

(LeoE. Klopfer), 158 
Holton and Roller, Foundations of Modem 

Physical Science, 158 

Ice lens, construction of (activity), 141 

Incidence angle, 134-135 

Infrared photography (activity), 139 

Interaction of Color (Josef Albers), 175-176 

Interference, thin film, 138 

Interference pattern, of light, 136-137 

Intergovernmental Oceanographic Commission, 

175 
International Atomic Energy Agency, 175 
Isolated north pole (activity), 164 

Kennedy, President John F., address to N.A.S., 

175 
Knife-edge contact, current balance, 148 



Magnet, interaction with current-carrying wire, 
152-153 

soft, and isolated north pole (activity), 164 
Magnetic field, and deflection of electron beam, 
156 

effect on current-carrying wire, 147-154 

and generating electric current, 165 

measurement of intensity (activity), 158-159 

strength of, 154 
Maxima and minima, of reflected microwaves, 172 
Maxwell, James Clerk, first trichromatic color 

photograph, 139 
Meter, construction of (activity), 166 
Microwave (s), modulated, 174 

properties of 171-172 

reflected, interference of , /2— 174 

and signals, 174 
Microwave detector probe, 174 
Microwave generator, 171-172 
Microwave transmission systems (activity), 175 
MUlikan apparatus, 134 
Motor, construction of (activity), 167 
Modulated microwave, 174 
Modulated wave, 171 

Motor-generator demonstration (activity), 
167-168 

National Academy of Sciences (NAS), 100th 

Anniversary-, 175 
Neighboring Shore, The (Antonio Frasconi), 177 

Oscillator(s), turntable, 170 

Perpetual Motion and Modern Research for Cheap 

Power (R. Raymond Smedile), 159 
Perpetual motion machines (activity), 159-160 
"Perpetual Motion Machines" (Stanley W. 

Angrist), 159 
Photographic activities (activity), 139 
Photographing diffraction patterns (activity), 

138 
Photography, history of (activity), 139 
Physics for Entertainment (Y. Perelman), 141 
Physics of Television, The (Donald G. Fink and 

David M. Lutyens), 177 
Picket fence analogy, and polarized light, 141 
Plate, radio tube, 163-164 



184 



Poisson's spot (activity), 139 

Polarized Light ( W. A. Shurcliff and S. S. 

Ballard), 140 
Polarized light (activity), 140-141 

detection of (activity), 140-141 

picket fence analogy, 141 

uses of, 140 
Postage stamp honoring sciences, 175-177 

RCA Vacuum Tube Manual, 162, 164 
Radiation, electromagnetic, and microwave 
171-174 
and standing waves, 178 
Radio frequencies, 171 

Radio tube, components of (activity), 162-164 
Rainbow effect (activity), 139-140 
Refraction, of hght beam (experiment), 134-135 
Refraction angle, 134-135 
Resonant circuits, and frequency range, 171 

Scattered light (activity), 139 

Schlieren photography. Scientific American 

(February 1964) (activity), 139 
Science and the Artist— The story behind a new 

science stamp (activity), 175 
Science for the Airplane Passenger (Elizabeth A 

Wood), 140 
Science kits, Bell Telephone, 177 
Scientific American (May 1959, September 1959, 
January 1960), "Land effects," 140 
(February 1964), "SchUeren photography," 139 
(July 1962), "Telephone Switching," 177 
Signals, and microwaves, 174 



"Speech Synthesis," science kit, 177 

Speed of light in air, 137 

Standing electromagnetic waves (film loop), 178 

Surface, determining flatness of, 138 

"Telephone Switching," Scientific American 

(July 1962), 177 
Thin film interference (activity), 138 
Thomson, J. J., cathode ray experiments, 157 
Total internal reflection, 135 
Transistor amplifiers (activity), 163 
Trichromatic color photograph, first (James Clerk 

Maxwell), 139 
Turntable oscillators, and wavelength, 170-171 

Vacuum tubes, diode and triode characteristics of 

(activity), 161-162 
Verine, Jules, The Adventures of Captain Hatteras 

141 
Versorium, Gilbert's (activity), 158 
Voltaic pile, construction of (activity), 158 

Water, and light refraction, 135 
Waves, and communication (experiment) 
170-174 

modulated, 171 

standing electromagnetic, 178 

see also microwaves 
Waves and Messages (John R. Pierce), 177 
Wavelength, hght, 136-137 

Young's experiment— The wavelength of hght 
(experiment), 136-137 



185 



Answers to End-of-Section Questions 



Chapter 13 

Q1 No. Eventually diffraction begins to widen ttie 
beam. 

02 Romer based his prediction on the extra time 
he had calculated it would require light to cross the 
orbit of the earth. 

Q3 Romer showed that light does have a finite speed. 
Q4 Experiments carried out by Foucault and Fizeau 
showed that light has a lower speed in water than in 
air, whereas the particle model required that light 
have a higher speed in water. 
Q5 When light enters a more dense medium, its 
wavelength and speed decrease, but its frequency 
remains unchanged. 

Q6 Young's experiments showed that light could be 
made to form an interference pattern, and such a 
pattern could be explained only by assuming a wave 
model for light. 

Q7 It was diffraction that spread out the light beyond 
the two pinholes so that overlapping occurred and 
intereference took place between the two beams. 
Q8 Poisson applied Fresnel's wave equations to the 
shadow of a circular obstacle and found that there 
should be a bright spot in the center of the shadow. 
Q9 Newton passed a beam of white light through a 
prism and found that the white light was somehow 
replaced by a diverging beam of colored light. Further 
experiments proved that the colors could be recom- 
bined to form white light. 

Q10 Newton cut a hole in the screen on which the 
spectrum was projected and allowed a single color 
to pass through the hole and through a second prism; 
he found that the light was again refracted but no 
further separation took place. 
Q11 A shirt appears blue if it reflects mainly blue 
light and absorbs most of the other colors which 
make up white light. 

Q12 The "nature philosophers" were apt to postulate 
unifying principles regardless of experimental evidence 
to the contrary, and were very unhappy with the idea 
that something they had regarded as unquestionably 
pure had many components. 
Q13 The amount of scattering of light by tiny 
obstacles is greater for shorter wavelengths than 
for longer wavelengths. 

Q14 The "sky" is sunlight scattered by the atmos- 
phere. Light of short wavelength, the blue end of the 
spectrum, is scattered most. On the moon the sky 
looks dark because there is no atmosphere to scatter 
the light to the observer. 

Q15 Hooke and Huygens had proposed that light 
waves are similar to sound waves: Newton objected 
to this view because the familiar straight-line propa- 
gation of light was so different from the behavior of 
sound. In addition, Newton realized that polarization 
phenomena could not be accounted for in terms of 
spherical pressure waves. 

Q16 Reflection, refraction, diffraction, interference, 
polarization, color, finite speed and straight line 



propagation (this last would be associated with 
plane waves). 

Q17 No; only that light does exhibit many wave 
properties and that its speed in substances other than 
air does not agree with the predictions of a simple 
particle model. 

018 Light had been shown to have wave properties, 
and all other known wave motions required a physical 
medium to transmit them, so it was assumed that an 
"ether" must exist to transmit light waves. 

019 Because light is a transverse wave and propa- 
gates at such a high speed, the ether must be a very 
stift solid. 

Chapter 14 

01 He showed that the earth and the lodestone 
affect a magnetized needle in similar ways. 

02 Amber attracts many substances; lodestone only 
a few. Amber needs to be rubbed to attract; lodestone 
always attracts. Amber attracts towards its center; 
lodestone attracts towards either of its poles. 

03 1 . L/7ce charges repel each other. A body that has 
a net positive charge repels any body that has a net 
positive charge. That is, two glass rods that have both 
been rubbed will tend to repel each other. A body that 
has a net negative charge repels any other body that 
has a net negative charge. 

2. Unlike charges attract each other. A body that 
has a net positive charge attracts any body that has a 
net negative charge and vice versa. 

04 A cork hung inside a charged silver can was not 
attracted to the sides of the can. (This implied that 
there was no net electric force on the cork — a result 
similar to that proved by Newton for gravitational 
force inside a hollow sphere.) 

05 F^, a 1/fl-' and F^, « q,^q„ 

06 F^i will be one quarter as large. 

07 No, the ampere is the unit of current. 

08 Each point in a scalar field is given by a number 
only, whereas each point in a vector field is repre- 
sented by a number and a direction. Examples of 
scalar fields: sound field near a horn, light intensity 
near a bulb, temperature near a heater. Examples of 
vector fields: gravitational field of earth, electric fields 
near charged bodies, magnetic fields near magnets. 

09 To find the gravitational field at a point, place a 
known mass at the point, and measure both the direc- 
tion and magnitude of the force on it. The direction 
of the force is the direction of the field; the ratio of 

the magnitude of force and the mass, is the magnitude 
of the field. 

To find the electric field, place a known positive 
charge at the point, and measure the direction and 
magnitude of the force on the charge. The direction 
of the force is the direction of the electric field. The 
ratio of the magnitude of the charge, and the charge, 
is the magnitude of the field. 

Note: to determine the force in either case one could 
observe the acceleration of a known mass or 



186 



determine what additional force must be intro- 
duced to balance the original force. 
Q10 The corresponding forces would also be 
doubled and therefore the ratios of force to mass, 
and force to charge, would be unchanged. 
Q11 The negative test body will experience a force 
upward. 

Q12 If the droplets or spheres are charged 
negatively, they will experience an electric force in 
the direction opposite to the field direction. 
Q13 Charge comes in basic units: the charge of 
the electron. 

Q14 Franklin observed that unlike charges can 
cancel each other and he therefore proposed that 
negative charges are simply a deficiency of positive 
charges. 

Q15 It produced a steady current for a long period 
of time. 

Q16 The voltage between two points is the work 
done in moving a charge from one point to the other, 
divided by the magnitude of the charge. 
Q17 No; the potential difference is independent of 
both the path taken and the magnitude of the charge 
moved. 

Q18 An electron-volt is a unit of energy. 
Q19 If the voltage is doubled the current is also 
doubled. 

Q20 It means that when a voltage is applied to the 
ends of the resistor and a curi^nt flows through it, 
the ratio of voltage to current will be 5 x 10'"'. 
Q21 Apply several voltages to its ends, and measure 
the current produced in each case. Then find the 
ratios V/l for each case. If the ratios are the same, 
Ohm's Law applies. 

022 The electrical energy is changed into heat 
energy and possibly light energy. (If the current is 
cfianging, additional energy transformations occur; 
this topic will be discussed in Chapter 16.) 
Q23 Doubling the current results in four times the 
heat production (assuming the resistance is constant). 
Q24 The charges must be moving relative to the 
magnet. (They must in fact be moving across the field 
of the magnet.) 

Q25 It was found to be a "sideways" force! 
Q26 Forces act on a magnetized (but uncharged) 
compass needle placed near the current. The mag- 
netic field at any point near a straight conductor lies 
in a plane perpendicular to the wire and is tangent to 
a circle in that plane and having its center at the wire. 
The general shape of the magnetic field is circular. 
Q27 Ampere suspected that two currents should 
exert forces on each other. 
Q28 (b), (c), (d). 
Q29 (b), (c), (e). 

Q30 The magnetic force is not in the direction of 
motion of the particle — it is directed off to the side, at 
an angle of 90° to the direction of motion. It does NOT 
do any work on it, since it is always perpendicular 
to the direction of motion. 



Q31 Gravity always acts toward the center of the 
earth, and is proportional to the mass (it is indepen- 
dent of the velocity). 

The Electric Field acts in the direction of the field 
(or opposite to that direction for negative charges), is 
proportional to the charge on the object, and is 
independent of the velocity of the object. 

The Magnetic Field acts perpendicularly to both 
the field direction and the direction of motion, is 
proportional to both the charge and the velocity, 
and depends on the direction in which the object 
is moving. 

Chapter 15 

Q1 The single magnetic pole is free to move and it 
follows a circular line of magnetic force around the 
current carrying wire. 

Q2 Faraday is considered the discoverer of electro- 
magnetic induction because he was the first to publish 
the discovery, and because he did a series of 
exhaustive experiments on it. 

03 The production of a current by magnetism. 

04 The loop is horizontal for maximum current, 
vertical for minimum. The reason is that the coil is 
cutting lines of force most rapidly when horizontal, 
and least rapidly when vertical. 

05 It reverses the connection of the generator to 
the outside circuit at every half turn of the loop. 

06 It comes from the mechanical device which is 
turning the coil in the magnetic field. 

07 Use a battery to drive current through the coil. 

08 Batteries were weak and expensive. 

09 An unknown workman showed that Gramme's 
dynamo could run as a motor. 

010 Too glaring, too expensive, too inconvenient. 

011 An improved vacuum pump. 

012 A small current will have a large heating effect 
if the resistance is high enough. 

013 Cities became larger, since easy transportation 
from one part to another was now possible; buildings 
became taller, since elevators could carry people to 
upper floors; the hours available for work in factories, 
stores and offices became much longer. 

014 There is less heating loss in the transmission 
wires. 

015 A current is induced in the secondary coil only 
when there is a changing current in the primary coil. 

Chapter 16 

01 A magnetic field. 

02 The small displacement of charges that accom- 
panies a changing electric field. 

03 The four principles are: 

(1) An electric current in a conductor produces 
magnetic lines of force that circle the 
conductor. 

(2) When a conductor moves across externally 
set up magnetic lines of force, a current is 
induced in the conductor. 



187 



HOLT, RINEHART AND WINSTON, INC.