London penetration depth (${\lambda }_L=\sqrt{m/({\mu }_0{n}_s{q}^2)}$)

For uniform vortex-free superconductivity, the London equation and stationary Maxwell equations give ${\nabla }^2\mathbf{B}=\mathbf{B}/{\lambda }_L^2$. A field tangential to a planar superconducting half-space decays as $\mathbf{B}(z)=\mathbf{B}(0)e^{-z/{\lambda }_L}$. A nonzero normal boundary field is incompatible with this translation-invariant decaying Meissner solution, because divergence-free magnetic flux would require that component to remain constant.