86 WORK OF ELECTRICAL FORCES. 



The variation of energy is then 



w - w = I ax ! - v 2 ) v - (v - v 2 )v 2 + (v 



- vjvj 



The resultant F of the actions of A and B on C is, by symmetry, 

 parallel to the common axis; the work F#, performed during the 

 displacement x, is equal to the variation of energy. We get from 

 this 



We may, indeed, express the coefficient a in functions of the 

 data of the problem. We know, in fact (80), in the case of two 

 unlimited concentric cylinders, the radii of which are R and Rj and 

 the potentials V and V 1} that the charge of the inner cylinder for the 

 length x is 



R 



From this we get 



and therefore 



