Lorentz Force on Permanent Magnet Rings by Moving Electrical Conductors

This paper addresses the calculation of Lorentz forces generated by axially or radially magnetized ring magnets due to passing ferromagnetic conductors. The boundary value problem is solved using the Fourier transform while considering the interaction between the magnetic field of the ring magnet and the induced eddy currents. The Lorentz force and the induced eddy current density are evaluated in integral form, including modified Bessel functions of the first and the second kind. The famous creeping magnet problem where a magnet travels inside a conducting pipe is extended to ring magnets. The obtained expressions are evaluated and compared with the finite-element solutions. It is observed that radially magnetized ring magnets generate higher Lorentz forces compared with their axially magnetized counterparts. The described scenario is applicable in the framework of flow rate evaluation, non-destructive testing, or electromagnetic damping. We provide supplementary material in the form of MATLAB functions to efficiently analyze such problems in similar areas of application. The present contribution is of great interest for theoretical, pedagogical, and practical reasons.