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 field and charge distribution in a system of conductors. We first prove Thomson’s theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field; perfect conductors are perfectly diamagnetic. The results agree with currents in superconductors being confined near the surface. The theorem implies a generalized force that expels current and magnetic field from the interior of a conductor that loses its resistivity. Examples of solutions that obey the theorem are presented. Received 27 August 2010, Accepted 28 October 2010, Scheduled 2 December 2010 Corresponding author: Hanno Essén ([email protected]).