﻿Motion of Constant Electromagnetic Systems. 1117 



to the axis. For u cylinder of radius r within the current 

 sheet, we have 



2irrx A=7rr 2 B=7rr 2 x , 



c 



so that A= -r- = -. r 



2. c 



, 1 . 2ttIi; - 2ttIu 



and (Ai?) = -o— . rcose/ = — =- y. 



c s ' c 2 c 2 J 



Thus 



1 __, A N 27rlv Iron 



- -V(AtO = - ? -=^[Bu] 



is uniform within the sheet and is directed downward in the 

 figure. 



The surface density of the charge which terminates the 



uniform field with intensity V(Ai>) is 



2ttIv a Iv n 

 cr-[ = - — «■ cos u = -7-0 cos v. 



The charges per unit length terminating this field on the two 

 hemi- cylinders are 



n via 



± ^ = <7 i ( e=oo r .) x2a=: - c r- 



The electric moment Q x of these charges, positive on the 

 upper half and negative on the lower half, is evidently 



~ C a a Iv , ira 2 Iv 



and is directed upward in the figure. The magnetic moment 

 of the system, per unit length, is 



c 

 directed into the paper in the figure. Thus 



Outside the sheet (?'>a), 



A 27rla 2 

 A= — — 

 cr 



, , 1 , . . 27rltt 2 t' cos 6 



and £=-(At>)=- ^ -. 



