130, 131] ELECTRICAL EQUILIBRIUM. 253 



The strength of electric field, or the intensity of electric force 

 at a point, F, is defined as the force acting on unit of electricity 

 placed at the point. Its dimensions are obtained from 



[Fe] = Force = 

 [F] = 



dV 

 This agrees with the definition F = - which is of dimensions 



Potentkl ^-4 



Length 



The energy of the system may be written in either of the forms, 

 118 (8), 



the integrals having dimensions 



[Surface-density x Potential x Surface] = [ML*T-*], 

 and [Volume-density x Potential x Volume], 



or, 118 (10), 



the integral having the dimensions 



[Field-strength 2 ] x [Volume] = [ML*T~ 2 ], 

 giving in either case the proper dimensions for energy. 



131. Electrical Equilibrium. Suppose we have an electric 

 field due to the presence of a number of charged insulating bodies 

 D, together with a number of conductors K, insulated and originally 

 either charged or not. The charges of the bodies D cannot move 

 in the bodies, since they are insulators. We shall assume that the 

 dielectric properties of the bodies D are the same as those of air. 

 The electrification of the conductors, however, may move in any 

 manner in the conductors, subject to the condition that the total 

 charge e s of any conductor K s is constant. By the principle of 

 virtual work, we can find the condition for equilibrium. 



Suppose that in any assumed distribution V is the potential 

 due to the total electrification of the conductors K> in which the 

 volume and surface densities are p and <r. Let V be the potential 



