64 ELECTRICAL EQUILIBRIUM. 



Let R be the radius of the sphere A (Fig. 16), Rj and R 2 

 those of the concentric envelope B, which at first we will suppose is 

 insulated. If an electric charge M is given to the sphere A, the 

 envelope B acquires (58) a charge equal to - M upon its inner 

 surface S 15 and a charge + M upon its outer surface S 2 . The value 

 of the potential at the centre of the sphere is obviously 



M M M |~ i 



R~D "O I T) 



*i *l L ** 



The capacity C of the inner sphere being the charge which 

 corresponds to V = i, we have 



c R R, R 2 



The two layers +M upon the sphere, A, and -M upon the 

 surface S x , have a potential equal to zero on the outside. The 

 potential V x of the envelope B depends, then, solely on the outer 

 layer +M, and is the same as at the centre of the sphere S 2 , 

 supposed to be homogeneous, which gives 



If the envelope B is connected with the earth, its potential 

 becomes zero, the external charge + M disappears, and the capacity 

 of the sphere is then 



iii e 



C R Rj RRj 



e being the thickness of the dielectric. 



If the thickness of the dielectric is small in comparison with the 

 radius of the sphere, we may neglect the difference between R and 

 02 RR 



RI, and take instead of for the capacity. If this capacity 



e e 



be expressed as a function of the surface of the sphere, we have 



c = R 2 = 4'rR 2= _S_ 

 e 4 4 ' 



