CHAPTER XIV. 



INDUCTION OF CURRENTS IN LINEAR CIRCUITS. 



PHYSICAL PRINCIPLES. 



506. IT has been seen that, on moving a magnetic pole about in the 

 presence of electric currents, there is a certain amount of work done on the 

 pole by the forces of the field. If the conservation of energy is to be true of 

 a field of this kind, the work done on the magnetic pole must be represented 

 by the disappearance of an equal amount of energy in some other part of the 

 field. If all the currents in the field remain steady, there is only one store 

 of energy from which this amount of work can be drawn, namely the energy 

 of the batteries which maintain the currents, so that these batteries must, 

 during the motion of the magnetic poles, give up more than sufficient energy 

 to maintain the currents, the excess amount of energy representing work per- 

 formed on the poles. Or again, if the batteries supply energy at a uniform 

 rate, part of this energy must be used in performing work on the moving 

 poles, so that the currents maintained in the circuits will be less than they 

 would be if the moving poles were at rest. 



Let us suppose that we have an imaginary arrangement by which addi- 

 tional electromotive forces can be inserted into, or removed from, each circuit 

 as required, and let us suppose that this arrangement is manipulated so as to 

 keep each current constant. 



Consider first the case of a single movable pole of strength m and a single 

 circuit in which the current is maintained at a uniform strength i. If o> is 

 the solid angle subtended by the circuit at the position of the pole at any 

 instant, the potential energy of the pole in the field of the current is mio), so 

 that in an infinitesimal interval dt of the motion of the pole, the work per- 

 formed on the pole by the forces of the field is mi -77 dt. The current which 

 has flowed in this time is idt, so that the extra work done by the additional 



batteries is the same as that of an additional electromotive force m , 



dt 



