﻿780 Mr. B. B. Baker on the Path of an 



coordinates (w, y, z) by the relations 



x = rco&0, y — r sin Ocoscj), z — r sin sin (j> ; 

 the kinetic energy of the moving electron is therefore 



±m(r 2 + r 2 6 2 + r 2 sin 2 6 <j> 2 )> 



We have further to determine the potential energy of the 



system due to the mutual interaction between the electron 



and the magnetic wheel. To do this the magnetic wheel, 



when it is rotating with angular velocity ijk may be looked 



M-vjr 



upon as a magnetic current of strength ^ flowing in a 



circle of radius a. Now just as an electric current flowing 

 round a circuit may be replaced by an equivalent magnetic 

 shell bounded by the circuit, whose magnetic moment per 

 unit area is proportional to the current-strength, so we may 

 replace the magnetic current by an electric shell, bounded 

 by the circuit, such an electric shell being equivalent to a 

 chorged condenser in electrostatics. For convenience we 

 shall suppose the electric shell to have the form of a hemi- 

 sphere of radius a bounded by the circumference of the 

 magnetic wheel, the charge per unit area on either plate of 



the condenser being -^-. The electric potential at any 



point P due to the condenser is therefore ~£ . co, where co 



is the solid angle subtended by the magnetic wheel at the 

 point P. The potential energy V of the system is thus 



— ^- — ; it is independent of the coordinate d>, and may be 



expanded in powers of r in the form : 

 when r<a, 



Y = Myjre \ 1- -P^cos 6)+\ ~P 3 (cos $)-... 



L (i Z ci 



. . . . (i) 



when r>a, 



'la 2 -, „ x 1.3 



V = Mt4^ 2 P i( co ^)-^l^ P 3(cos^) + 



(-l)^+ 1 1.3....(2n-l) a 



2,1 



" ,+ 2.4. ...2n r 2n P 2n-l 



(cos 6) + ...]. 



(2) 



