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XXXIX. On the Electromagnetic Efects due to the Motion 

 of Electrification through a Dielectric. By Oliver 

 Heaviside *. 



1. ri^HE following paper consists of, First, a short discussion 

 X of the theory of the slow motion of an electric charge 

 through a dielectric, having for object the possible correction 

 of previously published results. Secondly, a discussion of 

 the theory of the electromagnetic effects due to motion of a 

 charge at any speed, with the development of the complete 

 solution in finite form when the motion is steady and recti- 

 linear. Thirdly, a few simple illustrations of the last when 

 the charge is distributed. 



Given a steady electric field in a dielectric, due to electri- 

 fication. It is sufficient to consider a charge g at a point, as 

 we may readily extend results later. If this charge be 

 shifted from one position to another, the displacement varies. 

 In accordance, therefore, with Maxwell's inimitable theory of 

 a dielectric, there is electi'ic current produced. Its time- 

 integral, which is the total change in the displacement, admits 

 of no question ; but it is by no means an elementary matter 

 to settle its rate of change in general, or the electric current. 

 But should the speed of the moving charge be only a very 

 small fraction of that of the propagation of disturbances, or 

 that of light, it is clear that the accommodation of the dis- 

 placement to the new positions which are assumed by the 

 charge during its motion is practically instantaneous in its 

 neighbourhood, so that we may imagine the charge to carry 

 about its stationary field of force rigidly attached to it. This 

 fixation of the displacement at any moment definitely fixes 

 the displacement-current. We at once find, however, that to 

 close the current requires us to regard the moving charge 

 itself as a current-element, of moment equal to the charge 

 multiplied by its velocity ; understanding by moment, in the 

 ca?.e of a distributed current, the product of current-density 

 an I volume. The necessity of regarding the moving charge 

 as an element of the " true current " may be also concluded 

 by simply considering that when a charge q is conveyed into 

 any region, an equal displacement simultaneously leaves it 

 through its boundary. 



Knowing the electric current, the magnetic force to corre- 

 spond becomes definitely known if the distribution of induc- 

 tivity be given ; and when this is constant everywhere, as 

 we shall suppose now and later, the magnetic force is simply 



* Communicated by the Author. 



