The Lorentz forces on an electrically conducting sphere in an alternating magnetic field

A method to calculate the Lorentz force on an electrically conducting sphere placed in an arbitrary sinusoidally varying magnetic field is developed. The crux of this method lies in expressing the external magnetic held and the eddy current density in the sphere in terms of a "source function" of the current sources and a "skin depth dependent function". The general formula for the Lorentz force is used to derive the special case of a sphere in an axisymmetric stack of circular current loops. Numerical results for this case are presented as a function of the stack geometry. Approximations of the skin depth functions for practical situations are presented. Finally, a procedure to determine the magnetic pressure distribution on the surface of a levitated liquid metal droplet is given.