produced by Motion in the Electric Field. 11 



We must now consider the case where \a and \a are both 

 large ; in this case we find from (6) and (7) 



n <oe i\a 



if \a/\a and A^/A^a 2 are both large. 



Thus the magnetic force parallel to x outside 



1 coe d cos {pt—\(r— a) \ 



~Zi^olTy~ r ' 



and that parallel to y 



1 (oe d cos {pt — \(r— -a)} 

 3 \ 2 a 2 dx t 



Thus, since X 2 a 2 is large, the magnetic force, though in the 

 same direction as that due to a current gov, is very much 

 smaller in magnitude, and fades away to zero as \a increases 

 without limit. 



b— 



8a2 da S °( Xia ) 



The maximum magnetic force inside the sphere 

 3D j- S (X 1 a)e^ = - 2| cos pt. 



Thus in this case the magnetic force just inside the sphere is 

 equal to — ve, while that outside the sphere is very much 

 smaller. This is a striking contrast to the previous cases, 

 where the magnetic force inside the sphere is very small 

 compared with that outside. Thus, in this case, when the 

 time of the oscillation is small compared with that of the 

 electrical oscillations the distribution of magnetic force is 

 turned inside out. The magnetic force diminishes very rapidly 

 as we recede from the surface of the sphere. In this case the 

 total current parallel to the axis of z inside the sphere is finite, 

 for this by equation (2) equals 



a- Jo 

 ip 2D47T . , 9 d a , . 



= — §#» cos pt. 



