On the Boundary Conditions for the Maxwell and London Electrodynamic Equations

In a superconductor placed in an external magnetic field, surface currents are produced and then distributed in a thin layer treated as the magnetic-field penetration depth. The constant current in a conductor of any type, together with the magnetic field, is forced out to the surface, which leads to the appearance of a so-called surface current. It is proposed that this current be considered as a bulk current flowing, however, in a thin layer. Since the layer thickness is independent of the material and the nature of the conductor, it is possible to assume that it corresponds to the depth of magnetic-field penetration into the superconductor in accordance with London's theory. The boundary conditions for the magnetic induction vector at the flat superconductor-free space interface are written taking this assumption into account. The magnetic induction and the current density experience a jump at the boundary. The obtained result makes it possible to calculate the surface superconductor energy, which turns out to be negative.