Relativity and the electric dipole moment of a moving, conducting, magnetized sphere

A classic experiment in the history of special relativity was designed to test the prediction that a moving magnetic dipole m develops an electric dipole moment p=v×m/c. In 1913 the competing theory was Lorentz’s electron theory. The experiment used a rotating magnetic medium composed of steel spheres embedded in wax. The results of the experiment agreed with the prediction of special relativity. A paper by Pellegrini and Swift reanalyzed the experiment using rotating coordinates. Their calculation disagreed with special relativity. One possible source of the disagreement is the nature of medium used in the experiment. This paper presents a straightforward calculation of the electric field of a steel sphere moving in a uniform magnetic field. The result demonstrates that any method of calculation consistent with Maxwell’s equations in the laboratory frame predicts a p=v×m/c contribution to the electric dipole moment. The calculations are carried out for a single moving sphere, while the Wilson experiment was done on an assembly of many spheres. We present arguments making it plausible that our result holds for such an assembly.