Physics – Classical Physics
Scientific paper
2010-05-30
Progress In Electromagnetics Research B, Vol. 27, pp.187-212, (2011)
Physics
Classical Physics
29 pages, 7 figures
Scientific paper
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.
Essen Hanno
Fiolhais Miguel C. N.
Nordmark Arne B.
Providencia Constança
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