Image of a static current loop over a superconducting sphere

The authors consider the boundary value problem in which the normal component of the magnetic field is zero at a spherical surface of radius α around the origin. They assume the source of the magnetic field to be a static current loop of radius ρ₁, whose center is on the z axis and lies in the plane z = z₁. The field inside the sphere is null. The field outside the sphere is solved by replacing the sphere by one image loop of radius ρ₂, whose center is on the z axis and lies in the plane z = z₂. The parameters of the image loop are derived by direct computation of the field at the spherical surface by using the Biot-Savart law. The present solution is related to the well-known image solution for a point charge over an equipotential sphere.