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MAGNETIC FIELD AND CURRENT ARE ZERO INSIDE IDEAL CONDUCTORS

By M. C. N. Fiolhais, H. Essen, C. Providencia, and A. B. Nordmark

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Abstract:
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.

Citation:
M. C. N. Fiolhais, H. Essen, C. Providencia, and A. B. Nordmark, "Magnetic Field and Current Are Zero Inside Ideal Conductors," Progress In Electromagnetics Research B, Vol. 27, 187-212, 2011.
doi:10.2528/PIERB10082701

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