Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/363

 a perfectly conducting sphere whose centre is at the point, the only change being that and  would now vanish inside the sphere. This inference was subsequently found to be incorrect: a distribution of electric charge on a moving sphere could in fact not be in equilibrium if the electric force were radial, since there would then be nothing to balance the mechanical force exerted ou the moving charge (which is equivalent to a current) by the magnetic field. The moving system which gives rise to the same field as a moving point-charge is not a sphere, but an oblate spheroid whose polar axis (which is in the direction of motion) bears to its equatorial axis the ratio {{Wikimath|(1 - v{{sup|2}}/c{{sup|2}}){{sup|$1⁄2$}}:1.

The energy of the field surrounding a charged sphere is greater when the sphere is in motion than when it is at rest. To determine the additional energy quantitatively (retaining only the lowest significant powers of {{Wikimath|v/c}}), we have only to integrate, throughout the space outside the sphere, the expression {{Wikimath|H{{sup|2}}/8π}}, which represents the electrokinetic energy per unit volume: the result is {{Wikimath|e{{sup|2}}v{{sup|2}}/3a}}, where {{Wikimath|e}} denotes the charge, {{Wikimath|v}} the velocity, and {{Wikimath|a}} the radius of the sphere.

It is evident from this result that the work required to be done in order to communicate a given velocity to the sphere is greater when the sphere is charged than when it is uncharged; that is to say, the virtual mass of the sphere is increased by an amount {{Wikimath|2e{{sup|2}}/3a}}, owing to the presence of the charge. This may be regarded as arising from the self-induction of the convection-current which is formed when the charge is set in motion. It was suggested by J. Larmor and by W. Wien that the inertia of ordinary ponderable matter may ultimately prove to be of this nature, the atoms being constituted of systems of electrons.