The Magnetic Inertia of a Charged Sphere in a Field of Electric Force

Abstract

DR. O. HEAVISIDE has investigated (NATURE, April 19) the slow motion of a charged conducting sphere through a uniform electric field, in a direction parallel to the electric force of the field, and has calculated the increase in the magnetic energy and inertia of the sphere resulting from the re-distribution of the charge under the influence of the field. His paper has suggested the following investigation, in which the slow motion of the sphere is at right angles to the direction of the electric field. But, as Dr. Heaviside has pointed out to me, this problem has no single definite solution. For, if the sphere, initially at rest in the field, be set in motion, the motion of the unequally distributed charges on the surface of the sphere will tend to give rise to magnetic force in the interior; but the magnetic force will only gradually penetrate into the interior, and electric curents circulating in the sphere in parallel planes will cause a magnetic force opposed to that due to the moving charges. If the conductivity be perfect, these currents will persist, and the interior of the sphere will be permanently free from either electric or magnetic force; but, with finite conductivity, the currents will die away, and the magnetic force will finally attain a definite value inside the sphere, although the electric force vanishes. In each of these cases a solution is easily found; but while the currents are dying away the magnetic energy gradually changes, and the calculation of the energy at any given time might be difficult. I therefore confine myself to the two limiting cases. The case of the final stage when there is finite conductivity I had solved when Dr. Heaviside suggested to me that I should include the case of infinite conductivity in my investigation. The present communication is the outcome of that suggestion.