MUTUAL INDUCTION OF TWO LONG COILS. 



137 



The total number of turns being n nji, we may write, 



(35) 



If the angle # is very nearly a right angle that is to say, if 

 the ratio of the distance OP to the semi length - of the cylinder 



2 



is very great we have sensibly 



and therefore 



which was obvious (153). 



nS 



r 3 



Fig. 142. 



In order to obtain the action of a coil of thickness 2^, the value of 

 X must be expanded in increasing powers of - , then multiplied by 

 n^da.) and integrated between the limits a - c and a + c. 



770. MUTUAL INDUCTION OF Two LONG COILS. The value of 

 the action in the interior of such a coil, if it were indefinitely long 

 (551), would be 47r 1 ; its coefficient of induction on a parallel coil 

 C' with the same axis in the interior of section S', and with n' turns, 

 would be expressed by 



M = 



If the coil has a finite length, the flow of induction corresponding 

 to the two bases must be subtracted from this value. 



In order to treat the problem directly, we may first assume that the 

 coil C', having the same axis as the first, is on the outside (Fig. 142). 



