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 = 0 everywhere so κ = 0. In that case the fluxoid is equal to the magnetic flux (Φ = Φ). If v = 0 Eq. () reduces to
Taking the rotation gives
Using the well-known relations  and  shows that the magnetic field in the bulk of the superconductor is zero as well. So, for thick rings, the total magnetic flux in the loop is quantized according to