Analysis and Numerical Simulation of Magnetic Forces between Rigid Polygonal Bodies. Part I: Analysis

Abstract. The analysis of magnetoelastic phenomena is a field of active research. Formulae for the magnetic force in macroscopic systems have been under discussion for some time. In [PPS], we rigorously justify several of the available formulae in the context of rigid bodies in two and three space dimensions. In the present, second part of our study, we investigate these formulae in a series of numerical experiments in which the magnetic force is computed in dependence on the geometries of the bodies as well as on the distance between them. In case the two bodies are in contact, i.e., in the limit as their distance tends to zero, we focus especially on a formula obtained in a discrete-to-continuum approximation. The aim of our study is to help clarify the question which force formula is the correct one in the sense that it describes nature most accurately and to suggest adequate real-life experiments for a comparison with the provided numerical data. 1