Magnetic field and current are zero inside ideal conductors

Authors: Fiolhais, C. N., Essén, H., Providencia, C., Nordmark, A.
Document Type: Article
Pubstate: Published
Journal: Progress In Electromagnetics Research B
Volume: 27   187-212
Year: 2011


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.