﻿Plane, Cylindrical, and Spherical Current Sheets. 205 



00 00 00 



n °-))j { ( . l .-^ + ( y -^ + (,-z o) n i '- • • (18) 



— oc — oo 



H' = - fi - f \h f dz Q f f RF(> y c t) 



J _oo */0 »/ — 00*^— 00 



g --"o- 1{ C— r ) r<te dyo. (10) 



^*_, (( )t + (y_ yo )t + (,_ J s6 _R( t _ T ))»}. 



If now the inducing system consists of a single pole of 



strength j\t) which moves about in any manner so that 



its coordinates at any time t are f (£), rj(t), £(0> functions of £, 



we have _,. 



F(d? y 2'oT)=0, 



except when a? =f(r), ?/ = t;(t), c = ?(t), and then 



F (# y -o t) £&?o <i?/o <feb =/( T ) • 

 Therefore 



n ° = K.*-^) 2 +(y-^)) 2 +(--?(0) 2 "P ' ' ' ' (20) 



This is the expression for the magnetic potential due to the 

 induced currents on the negative side of the sheet, i. e. on the 

 opposite side to the moving pole ; and it is to be observed that 

 z is taken to be negative on this side. 



The quantity CI 11 , which represents the potential due to the 

 induced currents on the positive side (where z is positive) , is 

 given by 



fl ,_ M 



R ,, , Z-hf(T) + R(i-T) 



. /W {(*- f(T)) , + (y-^(T)) i +(* + ?(T) + E(«-T))'}* dT ( " 2) 



and the complete expression for the potential due to the 

 induced currents and the moving pole itself is, by (4), 



10. The components of magnetic force at (x,y,z) due to 

 the induced currents alone are respectively 



dCL" da" dQ," m 



dx 9 dy ' dz ; 



z 



