Minimum magnetic energy theorem predicts Meissner effect in perfect conductors

Details Minimum magnetic energy theorem predicts Meissner effect in perfect conductors Minimum magnetic energy theorem predicts Meissner effect in perfect conductors

2009-12-08

arxiv.org/abs/0912.1579v1

Physics

Condensed Matter

Superconductivity

29 pages, 2 figures

Scientific paper

A theorem on the magnetic energy minimum in a perfect, or ideal, conductor is proved. Contrary to conventional wisdom the theorem provides a classical explanation of the expulsion of a magnetic field from the interior of a conductor that loses its resistivity. It is analogous to Thomson's theorem which states that static charge distributions in conductors are surface charge densities at constant potential since these have minimum energy. This theorem is proved here using a variational principle. Then an analogous result for the magnetic energy of current distributions is proved: magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field. The result agrees with currents in superconductors being confined near the surface and indicates that the distinction between superconductors and hypothetical perfect conductors is artificial.

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