On levitation of diamagnetic bodies in a magnetic field

Various methods for calculating the force characteristics of a suspension ensuring levitation of diamagnetic bodies of various origin and shape are considered. The method of calculation is based on the computation of the energy of interaction of a body upon its displacement from the center of suspension for an arbitrary configuration of the suspending field. The method of quasi-homogeneous approximation is considered and compared with the method for calculating the force characteristics based on the general formula for the magnetic energy. The necessary and sufficient conditions for conservative stability of the equilibrium state are formulated, and the stability domain is determined. It is shown that the stability domain depends on the size of the body. Calculations of force characteristics are performed specifically for the suspension of a diamagnetic sphere. The dependences of forces and stiffnesses on the magnetic field strength are obtained, which makes it possible to analyze the stability of confinement of the diamagnetic sphere in the field of the system of circular currents.