Levitation of permanent magnet ball

The paper presents approaches to the levitation of permanent magnet levitation in a forced inhomogeneous magnetostatic field. For a permanent magnet ball, the magnetic field distribution is derived in analytical forms using the separation of variables separation method. Distribution is given by power functions and Legendre polynomials. The force (i.e., material force) is caused by the vertical magnetization of a permanent magnet and reluctivity change at the magnet boundary. The levitation force is evaluated using the generalized Maxwell stress tensor, coenergy, material force density, and equivalent magnetic dipole methods. The levitation forces are presented in terms of both magnetic permeabilities. The stability of the equilibrium point is investigated. The frequencies of free and damped oscillations are evaluated.