INTERACTIONS OF MOVING ELECTRONS 215 



Let us now maintain the two currents by two separate 

 batteries. The forms of the two circuits obtained by 

 using the plane are identical and both have the same 

 inductance. Let us, however, represent the induc- 

 tance of each circuit by its proper subscript. The 

 energy represented by \Li? above then becomes \Lii-f ; 

 and similarly ^L 2 iz 2 . These are evidently the energies 

 which the circuits would possess if they were isolated 

 in space. 



But what about the energy represented by Life ? Is 

 it intrinsic to circuit 1 or to circuit 2? Obviously it 

 is a mutual energy. Let us therefore write it as Mi^ 

 indicating by the M that it is mutual. The total energy 

 of the system may now be represented as 



K.E. = tLM+SLttf+Mite (7) 



Which circuit has contributed this mutual energy? 

 The answer is : both circuits. For example, if we 

 allow the current to become established in circuit 1 

 and then attempt to establish the current ^ we find 

 that the acceleration of the electrons hi circuit 2 has 

 been accompanied by a retardation of those of circuit 

 1. Additional energy, therefore, must be supplied to 

 circuit 1 to maintain the velocity of its electrons. 

 The value of M may, however, be negative, 1 depend- 



1 If motion of the coils occurs, M changes in value. If it does, 

 the kinetic energy of electrons is converted into kinetic energy of 

 the ponderable coils or vice versa. In the first case (that of p. 211) 

 it may be shown that to maintain the currents the battery sources 

 must supply an increase of k.e. of electrons equal to twice the 

 external work done by the moving coils. In the second case the 

 source of mechanical energy supplies twice the decrease in k.e. of 

 the electrons. 



