﻿1114 . Mr. S. J. Barnett on Electric Fields due to the 



at any point of the system where the current density is I, we 

 obtain from (6) and (10) the relation 



*=f?4!^ 



„=f . ......... (12) 



This result was obtained from Clausius's theory in 1880 by 

 E. Budde * ; the corresponding result with the correction 

 for the second-order term in v/c was obtained by Lorentz f 

 in 1895, and by Silberstein f , from Minkowski's equations, 

 in 1914. 



From (12) it is easily shown that in the general case the 

 electric moment Q of the charges developed by the motion is 

 equal to 1/c multiplied by the vector product of the velocity 

 and the magnetic moment M ; that is, 



Q=-[>M], (13) 



6 



of which a number of special cases will be found below §. 



§ 3. Two infinite plane parallel current sheets B and C with 

 equal and opposite currents, I per unit length, in motion 

 parallel to the stream-lines (fig. 1). From (10) it is clear 



Fig-. 1. 



B 



D—k 



^=T 



: v 



-I 



that A = over the central plane D parallel to the sheets, 

 and that elsewhere it has the direction of the current in the 

 nearer sheet. Ty obtain the vector potential at a point P 



* E. Budde, Ann. der Phys. x. p. 553 (1880). 



t H. A. Lorentz, ' Versuch; 1895, §25. 



X L. Silberstein, < The Theory of Relativity,' 1914, p. 272. 



§ Equations (6) and (12) have both very recently been derived for a 

 special case by W. F. G. Swann, who does not refer to the earlier work 

 l>y Maxwell and the others mentioned above. He has also obtained ^13) 

 for the special case of a doublet, but with the wrong sign. See Phys. 

 Rev. xv. p. 365(1920). 



