Plasma-frequency form of London penetration depth
= Plasma-frequency form of London penetration depth
{title2=$\lambda_L=c/\omega_p$}
For carrier <number density> $n$, charge $q$ and effective <mass> $m$, the <plasma frequency> is $\omega_p^2=nq^2/(\epsilon_0m)$. Combining the second <London equation> with the <magnetostatic Ampère law> and <Gauss's law for magnetism> gives $\nabla^2\mathbf B=(\omega_p^2/c^2)\mathbf B$. Therefore the decaying planar solution has length $\lambda_L=c/\omega_p=\sqrt{m/(\mu_0nq^2)}$.