﻿466 Mr. W. M. Hicks on the Self-induction 



When small this becomes 



-tM-W 



7. The case of uniform current-density is of more practical 

 importance, as it leads to the case of a uniformly-wound 

 circular coil whose cross section is also circular. The mathe- 

 matical treatment, however, does not lead to such a complete 

 solution as in the former case. 



As the current-density is uniform, <7 = I/7rr 2 , and the right- 

 hand side of equation (1) is — 87rIp/V* 2 . 



A particular integral is 



-■81, 1 87rIa 3 S 3 



^ ioia u o" f* cosnv 7 

 F„ = s-a— - — rrdv. 



r *-r ~ */(C-c) 3r\G-c)V 

 whence 



16Ia 3 S 3 C n cosnv 

 W^ Jo (C-c)l 

 Now 



whence it is easy to show that 



6W2Id 

 F =- 



(sq;;-cq;), 



> . . . (9) 



also F 0= -^|^(sQ-CQ;); J 



f: 



64^/2 1 a 3 



(Q:-Qn) 



97' 2 



Substituting in 'R n F' n — 'B! n F n , and remembering that 

 SQ , l + CQ'„-(^-^)sQ a = 0, 



it will be found that 



! 



B = 



64*/2Ia J 



9wr- 



{ctP.QL-F.QJ+StF.QLl-P.Q:) 



»7rr 

 64^/2Ia : 



ft. (*»y), 



