Electromagnetic AC and impulse levitations of conductive, dielectric, and magnetic ball

The paper presents an analytical solution of levitation problem for conductive, dielectric and magnetically anisotropic ball. The levitation exerts either an AC or impulse magnetic field. Both the Lorentz and material electromagnetic forces (of magnetic matter) could lift the ball in a gravitational field. The electromagnetic field distribution is derived by means of variables separation method. The total force is evaluated by Maxwell stress tensor (generalized), co-energy and Lorentz methods. Additionally, power losses are calculated by means of Joule density and the Poynting vector surface integrals. High frequency asymptotic formulas for the Lorentz force and power losses are presented. All analytical solutions derived could be useful for rapid analysis and design of levitations systems. Finally, some remarks about considered levitations are formulated.