CHAP, iv.] ELECTRICITY AND MAGNETISM. 



102), will represent the exterior coating. Let the radii 



of these spheres be r and r' 



respectively. Suppose a charge 



of Q units to be imparted 



to A ; it will induce on the 



inner side of B an equal 



negative charge Q, and to 



the outer side of B a charge 



+ Q will be repelled. This 



latter is removed by contact 



with " earth," and need be 



no further considered. The 



potential 1 at the centre M, 



calculated by the rule given 



in Art. 238, will be 



V M = S 



" 1 



Fi - I02 



At a point N, outside the outer sphere and quite near to 

 it, the potential will be the same as if these two charges, 

 + Q and - Q, were both concentrated at M. Hence 



V N = ta=s = o. 



So then the difference of potentials will be 



whence 



But, by the preceding Article, the capacity C = y ^ y ^ 



therefore C .= -. 



We see from this formula that the capacity of the 

 condenser is proportional to the size of the metal globes, 

 and that if the insulating layer is very thin, that is, if 

 r be very nearly as great as r' t r' r will become very 



1 The student must remember that as there is no electric force within a 

 closed conductor the potential at the middle is just the same as at any other 

 point inside ; so that it is somewhat a stretch of language to talk of the 

 middle point M as having a potential. 



