﻿J Lot ion of Constant Electromagnetic Systems. 1121. 



in conformity with (12). The total charges upon the hemi- 

 spheres are 



, , v 7ra 2 Ir 



± 7 = X (ft + ?i) = ± — 7~- 



and the moment of the charges is 



Q l + Q 1 =Q=-[»M], 



Within the sphere. 



t>3A, 



47rlr 



- (.V)A- - {(t-V)A} y = - y = - 3 ^.-.^ [&]; 

 which is equal to the intensity ~ A(Av). 



Outside the sphere V(Av) is not everywhere even in 



' 11 



the same direction as the total intensity -TBi/] . - (rV)A 



- c c 



is again the intensity of a solenoidal field without 

 divergence whose flux through the sphere doubles the 



intensity inside and makes it every w r here equal to - [Br]. 



§8. Two cylindrical coaxial magnetic poles with a radial 

 magnetic field between them, and in motion parallel to the 



Fiff. 3. 



'oar/7 



axis (fig. 3). In this case the vector potential vanishes over 

 the central symmetrical plane of the field. The lines of 

 vector potential are circles, centred on the axis and normal 

 thereto. The magnetic flux across a cylinder of radius r and 

 length a?, one end in the symmetrical plane, is 27rr.rB = 



2iTrA; so that A = B.r= where C is a constant. To one 



