THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



JULY 1889. 



I. On the Magnetic Effects produced by Motion in the Electric 

 Field. By J. J. Thomson, M.A., F.R.S* 



IN the April number of the Philosophical Magazine 

 Mr. Heaviside discusses the question of a moving elec- 

 trified sphere, and while agreeing with the results I obtained 

 some time ago as to the magnetic force produced by such a 

 sphere when moving slowly, differs as to the numerical mag- 

 nitude of the energy possessed by the sphere and the forces 

 acting upon it when placed in a magnetic field. The latter 

 quantities, however, do not depend merely upon the alterations 

 caused by the motion of the sphere in the polarization of the 

 dielectric surrounding the sphere, but also upon the boundary 

 conditions we adopt and upon the view we take of the motion 

 close to the sphere of the medium in which the electric dis- 

 placements occur. 



Tins will be seen in the course of the following investigation, 

 in which I have endeavoured to take into account the motion 

 of the medium in which the displacements occur. I find that, 

 in order to close the circuits in this case, it is necessary to 

 assume effects which, as far as I know, have not been 

 noticed. 



Let us consider the case when the electric field is that due 

 to a charged sphere moving parallel to the axis of z with the 

 velocity w , the components at (.#, y, z) of the velocity of the 

 medium being u, v, w ; then, if we supposed that the dis- 



* Communicated by the Author. 

 Phil, Mag. S. 5. Vol. 28. No. 170. July 1889. B 



