PARTICULAR CASES OF INDUCTION. 



If the first coil contains a soft iron core of revolution about 

 the same axis, and of section S', the value of g is then 



When the core fills the whole cavity of the solenoid this value 

 reduces to 



)/? 



In this case the coefficient of mutual induction on an external 

 wire which makes ri turns, is 



(57) 



(Vs 



J- 1 



and the coefficient of self-induction of the coil itself, which contains 

 2irn turns, is 



(58) L=87T 2 ^(l+ 4 7r) ^ 



We have seen (502) what are the values of the integral I - 

 in certain special cases. J x 



556. ELECTRICAL MOTORS. Electrical motors are machines 

 containing conducting wires, electromagnets, or permanent magnets, 

 and so arranged that when a current produced by an extraneous 

 source is introduced, the electromagnetic or electrodynamic actions, 

 exerted between the different parts, are used to produce a relative 

 displacement of these parts. The continuity of the motion is 

 obtained either by sliding contacts, or by commutators which 

 alter the direction of the current in the machine. 



These machines may be so made as to work uniformly when 

 the strength of the current is constant, as with Faraday's disc 

 (530); but more frequently the actions are periodic, and the 

 relative motion of the parts, whether oscillating or rotating, produces 

 an electromotive force of induction E of a periodic character ; in 



