Calculation and analysis of the magnetic force acting on a particle in the magnetic field of separator. Analysis of the equations used in the magnetic methods of separation

This paper presents the derivation of equation for calculating the magnetic force acting on a paramagnetic ball situated in a region of a nonuniform magnetic field. We suggest the method of its extrapolation to the case of a nonlinear medium - the case of a ferromagnetic ball found under the influence of the magnetic field which is varying in a certain properly defined range. An experimental setting intended for the measurement of the magnetic force is described as well. For the first time a rigorous proof of the isodynamic magnetic field inexistence, that is a field which generates a magnetic force having the same constant direction and the same constant magnitude at each space point, is given. Moreover, using the method of conformal mappings we derive the analytic expressions for the magnetic field strength calculation in the case of a multipole system. With their help, different important features of the magnetic field behavior in this case are elucidated. The latter is done in a wide region of the geometric parameter space of the magnetic system. The interpretations of different issues discussed in the paper are compared to those that seems to be widely accepted in the magnetic methods of separation branch.