534 PARTICULAR CASES OF INDUCTION. 



In order to obtain the coefficient of self-induction of a coil, 

 we may assume, for instance, that two identical coils are super- 

 posed, and we may determine what is then their coefficient of 

 mutual induction (512). If in this way we make in the preceding 

 equations 



we get 



(52) L = 



O 



554. COILS WITH A SOFT IRON CORE. Let us assume that 

 the inner coil contains a cylindrical core of soft iron of radius a, 

 the coefficient of magnetisation of which is k. The value of N 

 does not change ; but so long at least as we remain within the 

 limits within which magnetisation is proportional to the magne- 

 tising force, the magnetic induction in the space occupied by 

 the soft iron is equal (379) to the original value of the force 

 multiplied by i + 4wvfc. In the case of a solenoid the value of 

 g then becomes 



g 

 If the coil consists of several layers, we have 



it follows that 

 (53) M 



; 



- *,) X - *J + l w(y, - *,) 



When the iron core entirely fills the inner cavity, and the 

 two coils are in contact, we may put 



we get then 



(54) M = ^ **n\f%(z -y) (y - x) / + xy + ^ + i zM . 



