MAGNETIC FIELD AND CURRENT ARE ZERO INSIDE IDEAL CONDUCTORS

We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson's theorem on the equilibrium electric fleld and charge distribution in a system of conductors. We flrst prove Thomson's theorem using a variational principle. Our new theorem is then derived by similar methods. We flnd that magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic fleld; perfect conductors are perfectly diamagnetic. The results agree with currents in superconductors being conflned near the surface. The theorem implies a generalized force that expels current and magnetic fleld from the interior of a conductor that loses its resistivity. Examples of solutions that obey the theorem are presented.