74 Conductors and Condensers [CH. in 



and it is now possible to determine the constant C as soon as the potential 

 of either cylinder is known. 



Let V a , V b be the potentials of the inner and outer cylinders, so that 



V a = C-2e\oga, 

 V b = C-2e\ogb. 



By subtraction V a - V b - 2e log (- J , 



so that the capacity is 



"-' 



per unit length. 



Parallel Plate Condenser. 



83. This condenser consists of two parallel plates facing one another, 

 say at distance d apart. Lines of force will pass from the inner face of one 

 to the inner face of the other, and in regions sufficiently far removed from 

 the edges of the plate these lines of force will be perpendicular to the plate 

 throughout their length. If cr is the surface density of electrification of one 

 plate, that of the other will be a. Since the cross-section of a tube 

 remains the same throughout its length, and since the electric intensity 

 varies as the cross-section, it follows that the intensity must be the same 

 throughout the whole length of a tube, and this, by Coulomb's Theorem, 

 will be 4-7T0-, its value at the surface of either plate. Hence the difference 

 of potential between the two plates, obtained by integrating the intensity 

 along a line of force, will be 



The capacity per unit area is equal to the charge per unit area cr 

 divided by this difference of potential, and is therefore 



The capacity of a condenser formed of two parallel plates, each of area A y 

 is therefore 



A 



except for a correction required by the irregularities in the lines of force 

 near the edges of the plates. 



Inductive Capacity. 



84. It was found by Cavendish, and afterwards independently by 

 Faraday, that the capacity of a condenser depends not only on the shape 

 and size of the conducting plates but also on the nature of the insulating 

 material, or dielectric to use Faraday's word, by which they are separated. 



