﻿Motioti of Constant Electromagnetic Systems. 11211 

 charged by the motion as to have the electric moment 

 - [17*]. Thus the sphere becomes electrically polarized, with 

 polarization, or electric moment per unit volume, given by 



where the summation extends over the unit volume. The 

 field of this polarization gives the polar part of the external 

 field, and, together with the internal part of the solenoidal 



field, just balances the motional intensity [*'B] inside the 



system : or we may consider that the effect of the polarization 

 is neutralized by that of an equal and opposite polarization 

 due to the charges induced in the parts of the conductor 

 adjacent to the individual magnetons, and that the distribution 

 produced by the motional intensity gives the polar part of the 

 external field, which, together with the solenoidal part, just 

 balances the motional intensity *. 



§ 12. In the case of two similar infinitely long magnets with 

 rectangular cross-sections placed parallel with opposite poles 

 facing one another symmetrically and in motion parallel to 

 their lengths and normal to the lines of induction of the magnetic 

 peld, the vector potential is evidently zero over the central 

 plane parallel to the motion and normal to the pole faces. 

 It is everywhere parallel to the velocity ; and its direction 

 is related to that of the central part of the magnetic field 

 exactly as in the case of §3. Its magnitude is independent 

 of the coordinate parallel to the length. Thus 



M=-(„V)A=0; 



and the total intensit}- outside the substance of the magnets, 

 viz., 



lies in planes normal to the motion, or is two-dimensional 

 like the magnetic field. Within the magnets themselves the 

 total electromotive intensity is zero, and, as in §11, there is 



an electric polarization P=-[/'I] at points where the in- 

 tensity of magnetization is I. 



* See E. Budde, /. c. ante, and W. F. G. Swann. /. c. ante. 



