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GUI. Electric Fields due to the Motion of Constant 

 Electromagnetic Systems. By S. J. Barnett *. 



§1. TN this article Maxwell's equation for the electromotive 

 JL intensity, together with a theorem derived from it 

 in §600 of his Treatise, and hitherto but little used, will be 

 applied to the investigation of a number of simple but 

 fundamental fields. Some of these fields are well known, 

 some are new; all of them are worth considering from the 

 standpoint of Maxwell's theorem. 



Consider an electromagnetic system B which has a velocity 

 v relative to fixed axes C. Let E, E', B, B', i/r, yjr', and 

 A, A' denote the electromotive intensities, magnetic induc- 

 tions, electric potentials, and vector potentials observed at a 

 point P fixed in C by one at rest in C and by one moving 

 with the system B, respectively. The electromotive intensity 

 at P, or the force per unit charge upon an infinitesimal 

 charged body fixed at P, is, in Gaussian units, 



E =-^-v* a) 



to the fixed observer. To the moving observer it is 



E 



where 



The electromotive intensity at P, if fixed to the moving 

 system B, is 



F=B+i[»B]--t^-V+ + i[rB] . (4) 



to an observer in C, and 



F'=E'+j[,B']=-i(^')-V*' ... (5) 



to an observer moving with B. 



Assuming a principle of relativity according to which 



* From papers presented to the American Physical Society, Nov. 26, 

 1921, Feb. 25 and April 21, 1922. Communicated by the Author. 



