1 70 ADVANCED ELECTRICITY AND MAGNETISM. 



but this is the amount of work done by the electric field on g 

 coulombs of charge which is carried from p to an infinite distance; 

 therefore, dividing by q we get the work required per coulomb, 

 and this is by definition the potential at p. Therefore: 



F=*. (6) 



4T r 



where V is the desired potential at p in volts, the potential 

 being due to the charge of Q coulombs uniformly distributed 

 over the sphere S. 



1 01. Capacity of a condenser consisting of concentric metal 

 spheres with air between. Figure 114 shows a metal sphere of 



Fig. 114. 



radius RI surrounded by a hollow metal sphere of which the 

 inside radius is R 2 . The inner sphere carries a charge of + Q 

 coulombs and the inner surface of the outer sphere carries - Q 

 coulombs; and these charges are uniformly distributed over the 

 respective spherical surfaces because of the complete symmetry. 

 The two spheres constitute a condenser, and therefore: 



Q = CE (i) 



where C is the capacity of the condenser and E is the electro- 

 motive force or potential difference between the spheres. If we 



