TEANSACTIONS OF SECTION A. 



63 



takes place between A and B. 



(see § 4) 



_EQ"- 



Thus the energy of the system 

 1 ) 



1 



[a a 

 a and a' being the radii of A, and the inner surface of B 



The " capacity " C may be defined — as in the ordinary 

 theory — as such that, if Q be the charge, the energy stored nn 



in the condenser = i . .^ . 



Hence capacity = - — ^ ^''^ "^ 



E 



■a E 



Also the capacity of a sphere is equal to its radius x ~, for by 



E 



§ 4 the energy of a charged sphere 



4^ 



8. The case of two parallel plates is simpler 

 still. The plates are, as usual, supposed to be 

 very large compared to the distance between 

 them, so that the disturbing effect of the edges 

 may be neglected. Let s = area of either plate, 

 d = the distance between them, x = the displace- 

 ment. 



Then, the energy = ^ .'E . <; . d . x-. 



Let Q = charge on either plate ; then Q = ?.r. 



Hence the energy = -2- . E — ^ ; 



s 



.-. capacity = -^ . 



Also (differentiating energy) force of attraction 

 ^EQ2 



2s ■ 



Or, we may express the force of attraction in terms of the 

 difference of pressures, which is equal to Ed.x, l^eing the 

 spring back of a tube of unit area. 



Then, since the energy 

 .•. attraction 



2 . EfZ2' 

 V being the difference of pressures. 



The theory of images finds, of course, its place in this 

 method of treating the subject, as much as in the ordinary one. 

 But we have now this very great advantage : that the student 

 can form easily a mental picture of the problem, and roughly 



