﻿Motion of Constant Electromagnetic Systems. 1119 



These are the component intensities due to an axial line 

 doublet with moment equal and opposite to that already 

 obtained. Thus 



1 (rV)A- -V(Av)=0=i[Bv]. 



The field whose intensity is -(i'V)A is thus a circuital 



field without divergence whose flux cancels that due to the 



... 

 charges in the region outside the cylinder and doubles that 



due to the charges inside. 



§ 7. A spherical current sheet, with current I per unit length 

 of the diameter along the magnetic axis, in 'motion normal to 

 the magnetic axis. The magnetic field within the sphere is 

 known to be uniform, normal to the planes of the stream 

 lines, with induction 



B= ~W 



The vector potential is evidently tangential to circles centred 

 on the magnetic axis and normal to the magnetic axis. 

 Within the sphere, for a cylinder of radius r, 



A= — r 



5c 



and = - (Av) = 3 — r cos 6= ■— . y. 



Thus __ V (A D )^-_^- r =-[B e ]. 



That part of the surface density due to the charges which 

 terminate this uniform field is evidently 



6cr 



The total charge (terminating the uniform field) on each 

 hemisphere is 



9 ira 2 Iv 



and the moment of these charges is 



1 iira'Ir 



Qi=( 



a i . 2ira sin 6 . a cl6 . a cos 6= 



