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London's Equations

Mathematical equations describing the magnetic field around a current-carrying superconducting wire, central to understanding the Meissner effect.
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The statement of the theorem

Let Js\mathbf{J}_s be the supercurrent density and B\mathbf{B} be the magnetic field. The first London equation relates the supercurrent to the magnetic field: \nJs=−nse2mA=nse2mA\mathbf{J}_s = -\frac{n_s e^2}{m} \mathbf{A} = \frac{n_s e^2}{m} \mathbf{A} \n(where A\mathbf{A} is the magnetic vector potential, and nsn_s is the superfluid density). The second London equation describes the decay of the magnetic field inside the superconductor: \n∇2B=1λL2B\nabla^2 \mathbf{B} = \frac{1}{\lambda_L^2} \mathbf{B} \nwhere λL=mnse2\lambda_L = \sqrt{\frac{m}{n_s e^2}} is the London penetration depth.
Source: Wikipedia