London screening (${\nabla }^2\mathbf{B}=\mathbf{B}/{\lambda }^2$)

Combining the static London equations with the magnetostatic Ampère law and $\nabla \cdot \mathbf{B}=0$ gives the displayed bulk equation for a uniform superconducting carrier density. A planar boundary gives exponentially decaying field on the London penetration depth scale; boundary geometry and vortices require their corresponding field solutions.