CAPACITY OF PLANE CONDENSERS. 69 



The capacity of a cylindrical condenser for unit length is then 



i 



C = 



This is a problem of great practical importance, as it represents 

 the case of telegraph cables, which are made of conducting wires 

 surrounded by an insulator, which in turn is itself protected from 

 injury by a metallic coating. 



81. PLANE CONDENSERS. Consider two conductors bounded 

 by plane parallel surfaces S x and S 2 , at the distance e, and at the 

 potentials V x and V 2 (Fig. 19). At a distance from the edges, which 

 is very great compared with the thickness of the dielectric, the lines 

 of force are parallel straight lines perpendicular to the surface in 

 question. 



e 



Fig. 19. 



The electrical field between the two planes is then uniform ; the 

 force is expressed by 



F= l ~ 2 , 

 e 



and the density on the surface S is 



F V\ V 



4?r 47T 



The electrostatic pressure, that is to say the force exerted upon 

 unit surface, is 



/ = 2 -2 * (TLL^Y; 



it is proportional to the square of the difference of potential, and 

 inversely as the square of the distance. 



Suppose that a portion a, of the surface S, at a great distance 

 from the edges, is movable, and that, being in contact with the 

 general surface, so as to have the same potential, it is maintained 



