Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/360

 the location of the charge must produce a continuous alteration of the electric field at any point in the surrounding medium; or, in the language of Maxwell's theory, there must be displacement-currents in the medium. It was to these displacement-currents that Thomson, in his original investigation, attributed the magnetic effects of moving charges. The particular system which he considered was that formed by a charged spherical conductor, moving uniformly in a straight line. It was assumed that the distribution of electricity remains uniform over the surface during the motion, and that the electric field in any position of the sphere is the same as if the sphere were at rest; these assumptions are true so long as quantities of order (v/c)2 are neglected, where v denotes the velocity of the sphere and c the velocity of light.

Thomson's method was to determine the displacement-currents in the space outside the sphere from the known values of the electric field, and then to calculate the vectorpotential due to these displacement-currents by means of the formula

where S&prime; denotes the displacement-current at (x&prime;y&prime;z&prime;). The magnetic field was then determined by the equation

A defect in this investigation was pointed out by FitzGerald, who, in a short but most valuable note, published a few months afterwards, observed that the displacement-currents of Thomson do not satisfy the circuital condition. This is most simply seen by considering the case in which the system consists of two parallel plates forming a condenser; if one of the plates is fixed, and the other plate is moved towards it, the electric field is annihilated in the space over which the moving plate travels: this destruction of electric displacement constitutes a displacement-current, which, considered alone, is evidently not a closed