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

Abstract

The dipole–dipole interaction model is used to calculate the angulardependence of lateral and levitation forces on a small permanent magnetand a cylindrical superconductor in the Meissner state lying laterallyoff the symmetric axis of the cylinder. Under the assumption that thelateral displacement of the magnet is small compared with the physicaldimensions of the system, we obtain analytical expressions for thelateral and levitation forces as functions of geometrical parameters ofthe superconductor as well as the height, the lateral displacement andthe orientation of magnetic moment of the magnet. The effect ofthickness and radius of the superconductor on the levitation force issimilar to that for a symmetric magnet/superconducting cylinder system,but within the range of lateral displacement. The splitting in thelevitation force increases with the increasing angle of orientation ofthe magnetic moment of the magnet. For a given lateral displacement ofthe magnet, the lateral force vanishes when the magnetic moment isperpendicular to the surface of the superconductor and has a maximumvalue when the moment is parallel to the surface. For a givenorientation of the magnetic moment, the lateral force has a linearrelationship with the lateral displacement. The stability of themagnet above the superconducting cylinder is discussed in detail.