Mechanics of a magnet and a Meissner superconducting ring at arbitrary position and orientation

The force and torque exerted by a magnetic dipole on a superconducting ring (or hollow cylinder) in the Meissner state at arbitrary position and orientation are calculated using a Maxwell-London model previously proposed by the authors. The center of the ring is an unstable equilibrium point for the magnet. At this point the ring tends to align the magnet but tends to expel it for any small axial deviation from the center. There is also a non-monotonic and oscillatory dependence of the forces and torques on the position caused by the finiteness of the ring and a torque arises when the magnet is displaced both radially and axially from the center of the cylinder which corresponds to the experimental data. Therefore, the use of a magnet in a Meissner superconducting ring as a self aligning bearing requires a centered position and that the axial unstability to be compensated by additional mechanical means.