500 INDUCTION. 



523. ELECTRODYNAMIC INDUCTION. If the inducing system 

 were a constant current, we might replace it by the equivalent 

 magnetic shell, and thus bring it within the preceding case ; but in 

 consequence of reactions, the inducing circuit itself will be under 

 induction, and the strength of the current will no longer be constant. 

 If R' and L' are the resistance and the coefficient of self-induction 

 of the inducing circuit, and E' the electromotive force which it 

 contains, the strength of the current in the two circuits will be 

 determined at each instant by two simultaneous equations 



OiLi/CQRY. (E 



+LT). 



The complete solution of these equations generally presents 

 great difficulties, and in the next chapter we shall investigate the 

 simplest cases in which it can be obtained; but the differential 

 equations already suggest some important remarks. 



If we add these equations, after having multiplied the first by I 

 and the second by I', we get 



(16) (El + ET - RI 2 - RT 2 )<# = L/(MI' + LI) + IV(MI + LT). 



The left hand side represents the excess of the energy furnished 

 by the sources in the two circuits over the thermal energy expended 

 in the conductor. 



The right hand side may be written as follows : 



(17) - </(LI 2 + 2MII' + LT 2 ) + - IVL + Htf M + - I'VL'; 



it represents the total variation of the potential energy of the two 

 circuits, and the external work. 



524, INTRINSIC ENERGY OF THE CURRENT. If the circuits 

 are fixed both in form and position, the factors L, M, and L' are 

 constants ; the portion of the energy not converted into heat is 

 expressed by 



[~LI 2 LT 2 ~1 



+Mir+ 



_2 



