The first case is a thick ring in an external magnetic field (Fig. 3a). The currents in a superconductor only flow in a thin layer at the surface. The thickness of this layer is determined by the so-called London penetration depth. It is of μm size or less. We consider a loop far away from the surface so that v s = 0 everywhere so κ = 0. In that case the fluxoid is equal to the magnetic flux (Φ v = Φ). If v s = 0 Eq. (15) reduces to