Angular Dependence of Lateral and Levitation Forces in Asymmetric Small Magnet/Superconducting Systems

The dipole-dipole interaction model is used to calculate the angular dependence of lateral and levitation forces on a small permanent magnet and a cylindrical superconductor in the Meissner state lying laterally off the symmetric axis of the cylinder. Under the assumption that the lateral displacement of the magnet is small compared with the physical dimensions of the system, we obtain analytical expressions for the lateral and levitation forces as functions of geometrical parameters of the superconductor as well as the height, the lateral displacement and the orientation of magnetic moment of the magnet. The effect of thickness and radius of the superconductor on the levitation force is similar to that for a symmetric magnet/superconducting cylinder system, but within the range of lateral displacement. The splitting in the levitation force increases with the increasing angle of orientation of the magnetic moment of the magnet. For a given lateral displacement of the magnet, the lateral force vanishes when the magnetic moment is perpendicular to the surface of the superconductor and has a maximum value when the moment is parallel to the surface. For a given orientation of the magnetic moment, the lateral force has a linear relationship with the lateral displacement. The stability of the magnet above the superconducting cylinder is discussed in detail.