64 ADVANCED ELECTRICITY AND MAGNETISM. 



41. Definition of mutual inductance. Consider two adjacent 

 circuits, and let one circuit be called the primary circuit and the 

 other the secondary circuit to distinguish them. Let i\ be the 

 current in the primary circuit, and let i% be the current in the 

 secondary circuit. 



Let $2 be the magnetic flux* through the secondary circuit 

 due to a current of i\ abamperes in the primary circuit. // is 

 evident from Art. 18 that $2 is proportional to i\. Therefore 

 we may write : 



$2 = Mil (i) 



in which the proportionality factor M is called the coefficient 

 of mutual induction or simply the mutual inductance of the two 

 circuits. 



Similarly, we have: 



$1 = Mi 2 (2) 



It is shown in the next article that the coefficient M has iden- 

 tically the same value in equations (i) and (2). 



If ii changes it is evident that $2 will change M times as 

 fast as ii, because it is always M times as large as ii according 



d<&2 , f dii d$z 



to equation (i). Therefore -j- = M-J-. But e 2 = 7: 



according to Arts. 29 and 31. Therefore we have: 



where e 2 is the electromotive force induced in the secondary 

 circuit by the changing value of the current in the primary circuit. 

 Similarly we may show that : 



* = - Jiff (4) 



42. Kinetic energy of two circuits. The kinetic energy of 

 two circuits is given by the equation: 



W = iLtfV + Mi** + \L#{ (i) 



* Each part of the flux being counted n times, where n is the number of turns 

 of wire encircling that part of the flux. 



