Levitation Force Between a Small Magnet and Superconducting Sphere

Abstract

Based on the Meissner effect and the image method, we studied the interaction between a magnetic point dipole and a superconducting sphere. We obtained analytical expressions for the interaction energy and the levitation force when the dipole is in an arbitrary orientation. Our calculations show the validity of using the image method for a antisymmetrical superconducting sphere-magnet system. Results show that the energy and the force are maxima when the magnetic dipole is perpendicular to the surface of superconductor and minima when it is tangent to the surface. Furthermore, the force acting on the tip of a magnetic force microscope above a superconducting sphere was derived as a generalization of the levitation force acts on a point dipole.