Exact solution of the London equation in two dimensions

We point out that for many simple geometries, corresponding to coordinate systems in which the Laplacian and boundary conditions are separable, exact solutions of the London equation can be obtained. We then present the solution for a circular inclusion embedded in a homogeneous infinite medium. We illustrate how the magnetic field associated with a vortex is distorted by the boundary of the inclusion. We also calculate the self-induced Lorentz force the vortex feels because of the inhomogeneity and show that the vortex is attracted or repelled to the inclusion boundary depending on whether the penetration depth is larger or smaller than that of the host material.