82 STATIC ELECTRICITY 



that distribution must be uniform. Hence the potential n 

 distance r from the centre outside the sphere is, by Chapter III, 



provided that r is small compared with tin- distance t< tin- 



Two concentric spheres with equal and opposite 



charges Q. Let the radii bo a and b. Tho potential of the 

 innorsphoro is uniform and equal to that at tin- centre. >imv tin- 

 whole of the positive charge N distant // from the md 



the .whole of the negative charge is distant I>. \\e \\ 



V = 2<- = -y 



r a b 



Between the spheres, at r from the centre, tin- potential due to 

 the positive charge is - (Chapter III), while the potential due to 



the negative charge is still y. Then 



" ~r ~~ 1}' 

 The outer sphere has potential 



v = F - ? = a 



The capacity of the inner sphere U 



.,_ Q ab 



= <T~Q~b=-a 



These two eases show, as is indeed olnious from the definition, 

 that a capacity has the dimension of a length. 



Two oppositely charged parallel conducting plane 

 plates, the plates being a distance apart very small compared 

 with their linear dimension-. 



The distribution must satisfy the two conditions found to hold 

 in all electrified systems \\hon the charges are at rest, viz. (1 ) 

 intensity close to each surface in the space between the plates must 

 be normal to the surface, and (2) the intensity within the sub- 

 stance of the conductors must be zero. These conditions will be 

 practically fulfilled if the distributions are equal and opposite and 

 uniform over the two surfaces except near the edges, and the lines 

 of force and strain will then go straight a< :o plate 



except near the edges. For let P, Fig. 65, be a point between 



