﻿Motion of Constant Electromagnetic Systems. 1115 



between the sheets and distant y from D in the direction of 

 the sheet B, in which v and I have the same direction, we 

 may apply (11) to the area abed. We thus get A x bc = 



Bxbcxy = xbrxy; so that 



A = B#=— y. 



Similarly, we find for the region above B, 



. 4ttI h 

 A= c X 2 



and for the region below (J, 

 Between the plates 



4ttI h 

 A= x ^ 



4>=-(A.v)= -^-vy; 



so that - -V(Av) = -^ v= - [Bt?l 



c y c c L J 



is uniform and directed from B toward D. The surfaces of 



C and D have thus the charges + 2 and — -j per unit 



c c 



area, in agreement with the general relation (12). Outside 



4:77"ll?/i 



the region between the sheets </>= + — ——— and — V</> = 0. 



T^A 

 Here ^- = - (v\/)A = 0, so that the field is purely polar 



an( ] _. _ V(Ar) is the total electric intensity. 

 c 

 It is easy to see that if M denotes the magnetic moment 

 of the system, and Q its electric moment, 



Q= c Vm]. 



The charges developed by the motion, being themselves in 

 motion with velocity v, produce a magnetic field in the 

 ■direction of the original held and with intensity 



7 47T Iv TT v 2 



c c- c 2 



thus showing, in conformity with Larmor's statement, that 

 the adoption of Maxwell's method introduces an error of the 



4C2 



