REPRESENTATION OF THE ELECTRICAL FIELD. Ill 



CHAPTER VII. 



PARTICULAR CASES OF EQUILIBRIUM. 



127. REPRESENTATION OF THE ELECTRICAL FIELD. The con- 

 dition of an electrical field is defined at every point by the direction 

 and magnitude of the force. It may be represented either by equi- 

 potential surfaces or by lines of force. 



In the former case, equipotential surfaces are drawn which cor- 

 respond to the numerical values of the potential i, 2, 3 ....#, and 

 which, therefore, are such that the transference of unit electricity 

 from any given surface to the next following one, corresponds to a 

 unit of work. 



The force, at each point, is perpendicular to the equipotential 

 surface ; its mean value F x between two consecutive surfaces of the 

 orders n and n + i, at a distance of a from each other, is defined by 

 the equation 



The value of the mean force is therefore inversely as a. 



These surfaces may be represented by a graphic method. 



Take first the case of a single centre of force, a point charged 

 with a mass m. The potential at the distance r is 



the equation 



m 



determines the radius of the sphere, the potential of which is V. Let 

 V have the values i, 2, 3 . . . , and draw the corresponding spheres, 

 we shall have equipotential surfaces, whose potentials correspond to 

 the natural series of numbers. 



128. Let us now assume that several centres, of masses m, m', m" 

 act simultaneously ; the resultant potential at a point being the 



