RESIDUAL CHARGE OF CONDENSERS. 233 



density, which gives the equation 



from which we deduce 



p i dp 



A V = ATT = 



p c dt 



and therefore 



putting T = . 



This equation shows that the density p constantly decreases, and 

 that if for any reason the dielectric has received a charge in the 

 interior, it will not retain it indefinitely ; this charge will always 

 finish by being altogether on the surface, like that of a good con- 

 ductor evidently an a priori conclusion. 



242. RESIDUAL CHARGE OF CONDENSERS. The phenomena 

 of absorption and of residual charge to which dielectrics give rise 

 should not be considered as effects of their own conductivity. Let 

 us examine, from this point of view, the series of phenomena to 

 which the charge or the discharge of a condenser gives rise. 



Let C be the capacity of a condenser, R the resistance of the 

 dielectric, E the difference of potential of the two coatings at the 

 moment /, r the resistance of the circuit which joins the two coatings 

 on the outside ; let E be the electromotive force of a source inter- 

 posed in the circuit. The increase of charge G/E of the condenser 

 during the time dt, is equal to the excess of the flow of electricity 



"F "F "P 



dt furnished by the source, over the flow dt which traverses 

 r R 



the dielectric. From this we have the equation 



ETP TT //TT 



- & H, tf-C' 



and therefore 



putting Tj = 



