﻿588 Mr. S. Butter worth on the Coefficients of 



10. Mutual inductances of finite coils. 

 (a) Non-overlapping coils. 



By definition, N gives the mutual induction between two 

 semi-infinite solid coils o£ unit winding density, having 

 radii r and unity, the distance of their faces being z. If 

 the radii of the coils are a and h, the separation c, and the 

 winding densities n lt n 2 , then by dimensions the mutual 

 induction is 



^ 2 a 5 tf(|, J j) (39) 



with h<a. 



If b>a, then from the reciprocal properly 



- N fr -D«**(j. 1) ( 4 °) 



If the coils are hollow, and the inner and outer radii are 

 « 1? a 2 ; £j, & 2 respectively, then from the laws of combination 

 of mutual inductances, the mutual induction (M) is given by 



L \ a 2 a 2/ \ a 2 a 2-'J 



When the coils have the same radii (-41) becomes (using 

 (40)) 



M,^^^!)^^,^^^!). (41a) 



If in addition, the coils are in contact 



M/n 1 n 2 =(a 2 *+a 1 *)X(0, l)-2a/tf(0, ^) . (416) 



Now let the coils be finite and of lengths 2/ 1; 2/ 2 , the 

 distance of their mid-points being h. From the laws of 

 combination of mutual inductances Ave find 



M=M(A-Z 1 -Z 2 )+M(/* + Z 1 + y 



-Mp-t+y-MtA+li-W, . . (42) 



in which M(c) is given by (41). 



When the coils have the same length 



M.=M(h-2l) + M(h + 2l)-2MQi). . . (42a) 



