104
ON THE SELF-INDUCTION OF
[36
Thus altogether the terms in (2) of the second order involving log r yiel in (4)
' [greater of log p2 and log Pl] - ^ smaller of ^ and ... .(15)
"
The complete value of (4) to this order of approximation is found b addition of (8), (10), and (15).
By making p2 and /oj equal we obtain at once for the self-induction of current limited to the circumference of an anchor-ring, and uniformly dif tributed over that circumference,
—-2], ..................(16)
p being the radius of the circular section. The value of L for this case, whe p2 is neglected, was virtually given by Maxwell *.
When the current is uniformly distributed over the area of the Hectioi we have to integrate again with respect to p-^ and pz between the limits and p in each case. For the more important terms we have from (8)
1 /Y
— 11 dp^ dp22 [log 8a - 2 — greater of log p2 and log pj
i Q o i , 1 , 8a 7 = log 8a — 2 — log p + ~ = log - - — T......
A similar operation performed upon (10) gives In like manner, the first part of (15) yields For the second part we have
I ." F JJ
~ s~^y 11 dP*dP* I>maller of p*> Pi2] = - g|^a;
thus altogether from (15)
The terms of the second order are accordingly, by addition of (18) an (19),
-,2 f ftjy ] \
.(20)
Electricitij and Magnetism, §§ 692, 706. Also by (6), with m = 1,