66 ELECTRICAL EQUILIBRIUM. 



The preceding problem corresponds to the case of a spherical jar 

 of constant thickness ; the influence of the small zone, which must 

 be cut off from the outer surface, to allow of communication with 



the interior, may be neglected ; the capacity is therefore represented 

 g 



by , and the charge by the formula 



It is easily seen that this formula applies equally to a Leyden jar 

 of any form, of constant and very small thickness, the coatings of 

 which cover the whole surface outside and inside. 



Let Sj and S 2 (Fig. 17) be the two opposite surfaces of the two 

 coatings, V l and V 2 their potentials. As the outer coating completely 

 surrounds the inner one, the electrical masses on these two surfaces 



are equal, and of opposite signs (57). The value of the force for a 

 point P of the dielectric, or being the density at A of the inner 

 layer, is 



dV 



F = = 47TCT. 



dn 



As the thickness e is supposed to be very small, the differential 



dV V V 



is virtually equal to -, which gives 



dn c 



The charge of a surface element dS is o-dS, and the total charge is 



f Vj-Vs/VS 

 M = U/S = 2 . 



4^ I e 



