Levitation Force Between a Point Magnetic Dipole and Superconducting Sphere

The magnetic interaction between a point dipole and a superconducting sphere in the Meissner state is investigated in detail. It is demonstrated that the special case of perfect flux exclusion can be solved by the method of images when the dipole is vertically magnetized. The incorporation of a nonzero penetration depth is then made by developing the solution within London theory. The analytic solution, given in terms of an infinite series representation, is refined by exactly summing the perfectly diamagnetic response. Throughout, special cases of physical interest are discussed and applications to magnetic force microscopy and levitation are described.