Magnetic Fields in Superconductors and Ferromagnetic Materials

Abstract

A comparison is made between the treatment of magnetic fields in superconductors and normal materials. First some history is given, showing how early workers anticipated vortices. Later treatments tried to build a macroscopic theory using forces and torques on magnets. This was extremely unsatisfactory. Maxwell’s equations for normal materials are derived using average fields. The differences between the applied field, the demagnetising field, the local field on an atom and H are made clear. The derivation in superconductors follows a different path and uses the theory of Evetts. Simple and rigorous derivations of the forces on bodies and magnetic energies are derived, with comments on less satisfactory treatments. This is extended to thermodynamic potentials including the Ginzburg-Landau free energy.