Minimum magnetic energy theorem predicts Meissner effect in perfect conductors

TL;DR

This paper proves a classical magnetic energy minimization theorem for perfect conductors, providing a new explanation for the Meissner effect by showing magnetic fields are expelled due to energy considerations, similar to electrostatic charge distributions.

Contribution

It introduces a variational principle-based theorem that explains the Meissner effect in perfect conductors, unifying superconductors and ideal conductors under a common energy minimization framework.

Findings

Magnetic energy is minimized with surface currents and zero interior magnetic field.

The theorem offers a classical explanation for the Meissner effect.

Superconductors and perfect conductors are shown to be fundamentally similar.

Abstract

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.