| The London theory of superconduction is a phenomenological theory designed to model the two major phenomena of superconduction: the persistence of supercurrent in the absence of an applied electric field and the expulsion of magnetic flux from the bulk of the material. The London theory also predicts that the electric field must vanish inside of steady-state superconductors.;Keywords: London theory of superconduction, magnetic flux expulsion, supercurrent, electric field;We show that the steady-state London theory of superconduction may be derived, using the variational principle, by minimizing the total system energy, consisting of the magnetic field energy and of the kinetic energy of the moving supercurrent. We further extend the London theory by minimizing the relativistic total energy, consisting of both electric and magnetic field energies, as well as the work done on the supercurrent by the fields. For typical superconducting materials, such as Lead and Indium, we show that the first order relativistic effects in the magnetic field are eleven orders of magnitude smaller than the applied magnetic field, for a 1 Tesla applied field. We also show that an external magnetic field induces an electric field within a steady-state superconductor. The steady-state electric field acts as a central force on the supercurrent, in addition to that of the magnetic field, directing it along closed paths. We show for the first time that the induced electric field and the Fermi pressure on electron gas determine the resulting charge distribution, which is characterized by two penetration depths. Lastly, we show that an external electric field penetrates beneath the surface of a superconductor to a depth where the Fermi pressure exactly opposes the force it exerts on the charges. |
