﻿468 Mr. W. Iff. Hicks on the Self-induction 



■-J¥*~i*iKK$MS<**}. 



-j;>.i(i)*^!-K"-i)f];-M-i)0 

 "i?+t(«-i){f-j:^; 



where the functions outside the integral are functions of u Q . 

 It results that 



4ttRI 2 /3 s \ 512Rcos 5 « V/ , f ft Q' 2 



E = s — 7 + cosec 2 « ) - -^ r^— 2/3 i - 2 J^ 



3 \4 / 8l7rsm 4 a ^ n C g 



and that the self-induction 



^("-;xf-j»}. 



, 512Rcos 5 a v _ f.Q'2 



— ( -a +cosec 2 « ) + -ni r- r - 2/3 n < 4 J^L 



3 \4 / 8l7rsin 4 a n i S 



-(-4X1 -£ c #-)}- 



It is seen that the question is not completely solved, as the 



f * CO 2 

 integral I -~t du has not been evaluated, as in the pre- 

 ceding case. Its value can, however, be approximated to 

 when k is small. 



If it be denoted by X n , it can be shown that 



(2n+l) 2 X, l+1 -16nX„-(2n-l) 2 X n _, = 8n^QJ, 



a difference equation, which if solved in a series ascending 

 from Q w+1 would give X n . 



If we call the self-induction L, the energy is ^LP. 



If there are N turns of wire with a current i, 



i = m, 



and energy = ^WLi 2 , 



whence the self-induction of such a coil is N 2 L. 



8. For such a coil the values of the flux function are : — 



Outside, 



64v/2Rcos 3 «N*' 1 ^ -p 

 * = - -TO 2 * v(C^o«Acos™; 



