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Magnetic Field and Current Are Zero Inside Ideal Conductors

By Miguel C. N. Fiolhais, Hanno Essén, Constanca Providencia, and Arne B. Nordmark
Progress In Electromagnetics Research B, Vol. 27, 187-212, 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.


Miguel C. N. Fiolhais, Hanno Essén, Constanca Providencia, and Arne B. Nordmark, "Magnetic Field and Current Are Zero Inside Ideal Conductors," Progress In Electromagnetics Research B, Vol. 27, 187-212, 2011.


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