DEPARTMENT OF TERRESTRIAL MAGNETISM. 287 



II. Two plane parallel sheets with currents ± I per unit length, v being parallel 



to the stream-lines. Between the sheets the electric field is uniform and 



Iv 1 



normal to v, the charges per unit area being ± g= = t -^. Again E= — V(Av). 



III. An infinite uniform circular cylindrical current sheet, with magnetic 



moment M per unit length, and v normal to the axis. - (Av) is such as to pro- 



c 



duce a uniform field with intensity — [Bv] within the cylinder, and without 

 the cylinder the field of an axial electric line doublet with moment - [vM] per 



unit length. — (vv)A doubles the intensity inside and cancels it outside. 



IV. A spherical current sheet with magnetic moment M and current I per 

 unit length of the diameter, v being normal to the magnetic axis. Inside 



- (Av) gives a uniform intensity — v(Av)= — [Bv]; outside, the field of a 



c £0 



central electric point doublet with moment - [vM]. - (pv)A alters the in- 



1 c c 



tensity to — [Bv] everywhere. 



V. Two cylindrical coaxial magnetic poles with a radial field between them, 

 v being parallel to the axis. Here - (Av) =0, there are no charges, and 



E= ~(w)A=-[Bv]. 



VI. A conducting cylinder or sphere with uniform intensity of magnetization 



1 in motion normal to the magnetic axis. — All the formulae, for points outside 

 the system, are exactly similar to those for the cylindrical and spherical 

 current sheet, but I has now the meaning attached to it here instead of that 

 above. Within the material of the system, the electromotive intensity is 

 zero. The sphere or cylinder is electrically polarized, with polarization, or 



electric moment per unit volume, given by - [vl]. The field of this polariza- 



tion gives the polar part of the external field, and, together with the internal 



part of the solenoidal field, just balances the motional intensity - [vB] inside 



the system; or we may consider that the effect of the polarization is neutral- 

 ized 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 and also the polar part of the internal field, which, together 

 with the solenoidal part, just balances the motional intensity. 



VII. 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 field. The vector potential is zero over the central plane parallel 



to the motion and normal to the pole faces. It is everywhere parallel to the 



velocity. Its magnitude is independent of the coordinate parallel to the 



dA 

 length. Thus — = — (v v)A = 0, and the total intensity outside the substance 



at 



of the magnets, viz, E= — y(Av)=—[Bv] is polar and lies in planes normal 



