274 Prof. Townsend and Mr. Morrell on Electric 



If A be large compared with the radius a (h>20a), the 

 potential v Q at P due to the surface-distribution e per unit 

 length will be nearly the same as that due to a similar 

 distribution along the axis. The potential at P due to the 



C™ e 

 remote charges from Q to B may be taken as - dx. 



Jx <r 



If the limit x be at Q 2 the integral is negative, as the 



negative charge from Q 2 to Q 3 has a predominating effect ; 



but at some point Qx between P and Q 2 the integral is zero. 



From the tables of the values of the integral it can be seen 



• C 1 Zi 7> 



that the integral vanishes when the limit x is — ; — -= — 



approximately. Thus the potential at P is that due to 



charges within a distance —^ on either side, the total effect 



of the remoter charges being zero. 



Thus, when li is large compared with a, the potential v in 

 electromagnetic units is 



10+ V#7lOO + a 2 

 v = 2u*e log (7) 



or 



= 2w%log^ (8) 



approximately, u being the velocity of light. 

 Hence the capacity C is given by the equation 



C=^= L^ (9) 



In this value of C the specific inductive capacity of the 



cylinder has not been taken into consideration, and in order 



to correct for this effect it is necessarv to estimate the 



reduction in the value of v due to the induced charge on 



the surface of the cylinder. 



2irx 

 Since the potential v = v Q cos — ~ varies along the axis, 



t . • j- i . (K-l)X 

 there is an electric displacement ; per unit area or 



1 47T r 



the section due to the force X, and in the case of a solid 



