Magnetic energy and electron inertia in a superconducting sphere

The hypothesis that the magnetic energy of a current circuit is the kinetic energy of the effective conduction electrons, developed in a previous Monograph,1 is applied to the case of a conducting sphere without resistivity in a uniform magnetic field. A surface current is induced which prevents the growth of a magnetic field within the sphere, and expressions are found for the number and velocity of effective conduction electrons which carry the current. It is found that these electrons are in stable radial equilibrium, moving in circular orbits under the action of magnetic forces. The well-known Meissner effect in pure superconductors is shown to be an expected rather than an unexpected phenomenon, since its absence would require, under certain conditions, a supercurrent lacking equilibrium. The theory is shown to lead, by means of a simple assumption, to the basic equations of the London theory of superconductivity, but with a different interpretation of the velocity parameter. Finally, the inertial supercurrent and magnetic field which should be produced by the steady rotation of a superconducting sphere, as deduced by the new theory, are shown to be exactly the same as those forecast by the London theory.