CONDUCTORS AT CONSTANT POTENTIAL. 83 



but in the present case the last term is zero, for the charge is con- 

 stant on each of the conductors ; there simply remains 



A conductor originally in the neutral state would be drawn into 

 the electrical field. Hence the effect of the presence of this con- 

 ductor is to diminish the energy of the system. 



97. Conductors at Constant Potential. Let us now consider the 

 case of conductors kept at constant potentials by sources of elec- 

 tricity placed outside the field of action. 



We shall suppose that the various conductors A 15 A 2 , A 3 . . . , 

 charged with quantities M v M 2 , M 3 . . . , and to the potentials V 1? 

 V 2 > V 3 . . . , communicate separately with bodies of the capacities 

 Cj, C 2 , C 3 . . . , withdrawn from any external influence for instance, 

 closed condensers the outer coating of which is connected with 

 the earth. This case comes under that which we have been con- 

 sidering ; if W a is the energy of the conductors and W c that of the 

 condensers, the energy of the system is 



w=w a +w c . 



If the system undergoes any deformation without the intervention 

 of extraneous energy, the theorem (i) applies and gives 



(2) 

 The energy of the conductor is 



W a = - 



2 



and therefore 



2 2 



For the energy of the condensers, the capacity of which is un- 

 changed, we shall take the expression 



2 

 G 2 



