Interaction of a magnetic dipole with a slowly moving electrically conducting plate

TL;DR

This paper provides an analytical solution for the force and torque on a magnetic dipole near a moving conducting plate, extending previous models to arbitrary dipole orientations and serving as a benchmark for numerical simulations.

Contribution

It offers a comprehensive analytical framework for the force and torque on a magnetic dipole with arbitrary orientation near a moving conducting plate at low magnetic Reynolds number.

Findings

Explicit distributions of electric potential, eddy currents, and magnetic field derived.

All force and torque components can be calculated exactly without approximation.

Serves as a benchmark for numerical simulation validation.

Abstract

We report an analytical investigation of the force and torque acting upon a magnetic dipole placed in the vicinity of a moving electrically conducting nonmagnetic plate. This problem is relevant to contactless electromagnetic flow measurement in metallurgy and extends previous theoretical works (Thess et al. Phys. Rev. Lett. 96(2006), 164501; New J. Phys. 9(2007), 299) to the case where the orientation of the magnetic dipole relative to the plate is arbitrary. It is demonstrated that for the case of low magnetic Reynolds number the three-dimensional distributions of the induced electric potential, of the eddy currents and of the induced magnetic field can be rigorously derived. It is also shown that all components of the force and torque can be computed without any further approximation. The results of the present work serve as a benchmark problem that can be used to verify numerical simulations of more complex magnetic field distributions.