Abstract
An exact solution for a magnetostatic boundary value problem involving two fused (overlapping) spheres placed in a field generated by an axial magnetic point dipole is constructed based on the image method. The basic idea is illustrated for two unequal superconducting spheres intersecting with a vertex angle π/2 and the analytical solution for the scalar magnetic potential satisfying the Neumann boundary condition at the surface is derived. The image solution for a dipole-twin-sphere configuration consists of three image dipoles—one inside each sphere and the third inside a pseudo-/virtual sphere—all located at the respective inverse points inside the superconducting two-sphere assembly. The levitation force acting on the two-sphere superconducting surface is also calculated for the overlapping geometry. These exact results can be used as a benchmark for testing numerical algorithms for overlapping spherical superconductors. Our simple approach also offers clues for solving the Neumann boundary value problem for vertex angles π/n, n is an integer, and other related superconducting geometries.
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