The following paper is occupied by an attempt to investigate the distribution of the electric and magnetic forces which are called into play when certain electromagnetic systems are made to move with uniform velocity through the ether. Maxwell’s theory will be employed throughout, and will be applied to th e exact solution of several problems, and to the establishment of some results of a general nature. Professor J. J. Thomson was, I believe, the first to consider a problem of this sort, his paper giving the solution for the motion of a single electrical point-charge at a speed small compared with that of light. Mr. Oliver Heaviside next considered the question, and in his paper obtained an
exact
solution for the motion of a point-charge. He got the solution by means of the “vector potential” of the convection current formed by the moving charge. The mathematical analysis is of the symbolical kind, but it is shown that the result obtained by means of it satisfies all the necessary conditions. By integrations Mr. Heaviside obtains solutions for the motion of some simple cases of electrical distribution.
The Field Of A Step–Like Accelerated Point Charge: Liénard–Wiechert Potentials And Čerenkov Shock Waves Revisited