Page:ThomsonMagnetic1889.djvu/1



AND

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

By, M.A., F.R.S

the April number of the Philosophical Magazine Mr. Heaviside discusses the question of a moving electrified 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 magnitude 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 displacements occur.

This 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 $$w_0$$, the components at $$(x, y, z)$$ of the velocity of the medium being $$u, v, w$$; then, if we supposed that the displacement ''Phil. Mag.'' S. 5. Vol. 28. No. 170. July 1889.