﻿1118 Mr. S. J. Barnett on Electric Fields due to the 



This is the potential due to a line doublet situated on the 

 axis of the sheet with electric moment 



~ _ 7rla V 



per unit length and directed upward in the figure. 



Thus Q=-[>M]. 



The outward radial component of the intensity at the 

 surface of the cylinder due to the doublet of moment Q is 



^-^cos^= — g- cos#. Thus the surface density of the part 



of the charges on the cylinder terminating the outer field is 



°"2= 9-2 COS = (7! 



and its moment Q 2 = Qi. Thus the total electric moment per 

 unit length of the cylinder is 



Q=2Q 1= i|>M]. 



The total charge per unit length on the upper and lower 

 hemi-cylinders is 



In addition to the electric intensity — V(Av), there is 



also the solenoidal intensity 



1BA 1, _ A 



which does not vanish. Inside the cylinder 



so that the total intensity is - [Bv], 

 Outside the cylinder 



jK.viA}.-.^^(J)r : ^3 



and 



c l ' Jy c l Ox \r 2 J c 2 r 2 



