= London penetration depth
{c}
{title2=$\lambda_L=\sqrt{m/(\mu_0n_sq^2)}$}
{wiki}
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.
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