﻿Coefficients of Mutual Induction, of Coaxial Coils. 579 

 ,11 circle of radius p and centre at .;, 0), then 



<£>=-2tt P?~dp 

 o~ 







v-rrpX cf)(X)e-' x '~J 1 (\p)d\; . ... (4) 

 o 



•or on expanding Ji(Xp) in ascending powers of p and making 

 use of (3), 





•so that <f> can be found at all points if the potential at all 

 points along the axis of symmetry is given. 



Now let a solid coil of radius r extending from z to infinity 

 he placed with its axis along the axis of symmetry. The 

 number of linkages that the field makes with this coil is 



n = [ r d P r <f>dz 



nfin ,12a O 



. . (6) 



o 2 2n [2n + 3) \n \n + 1 dz 2n 



3. If n o is due to a second solid coil of unit radius extending 

 from z=Q to z= — co , then 



I2 = 27rj o ( v / /3 2 + ^~ / o)^ 



- 9r(«»logi±^ + t-2*), ... (7) 



where f 2 =l + ^ 2 . 



If c is large then (7) may be expanded in inverse powers 

 of z giving 



s = - v L_i ' - — r<o 



* 2*£ (s;+3)|« V+Tcso 3 " • • • w 



(9) 



so that 



1 d ' 2 " n o _ I V° f-)*l2(n+*) 1 

 2tt dz 2 » ~ 2^+1 J< (2s + 3) |j kt 1 (2c/" ' 



2 P 2 



