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We prove a theorem on the magnetic energy minimum in a system of perfect, orideal, conductors. It is analogous to Thomson's theorem on the equilibriumelectric field and charge distribution in a system of conductors. We firstprove Thomson's theorem using a variational principle. Our new theorem is thenderived by similar methods. We find that magnetic energy is minimized when thecurrent distribution is a surface current density with zero interior magneticfield; perfect conductors are perfectly diamagnetic. The results agree withcurrents in superconductors being confined near the surface. The theoremimplies a generalized force that expels current and magnetic field from theinterior of a conductor that loses its resistivity. Examples of solutions thatobey the theorem are presented.

New theorem of classical electromagnetism: equilibrium magnetic field and current density are zero inside ideal conductors