Magnetic Force Formulae for Magnets at Small Distances

PAMM 12/2005; 5(1):631 - 632. DOI: 10.1002/pamm.200510292


In [7], the magnetic force on subregions of rigid magnetized bodies was studied as a discrete-to-continuum limit. The derived force formula includes a new term, which depends on the underlying crystalline lattice structure ℒ. It originates from contributions of magnetic dipole-dipole interactions of dipole moments close to the boundary of the considered subregion.
Further studies of this new term have led to the question of how the magnetic force between two idealized magnets, which are a distance ε > 0 apart, depends on ε as ε → 0. In this article, analytical aspects of this question are discussed, cf. [5], where also numerical experiments are performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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    ABSTRACT: The mathematical and physical analysis of magnetoelastic phenomena is a topic of ongoing research. Different formulae have been proposed to describe the magnetic forces in macroscopic systems. We discuss several of these formulae in the context of rigid magnetized bodies. In case the bodies are in contact, we consider formulae both in the framework of macroscopic electrodynamics and via a multiscale approach, i.e., in a discrete setting of magnetic dipole moments. We give mathematically rigorous proofs for domains of polygonal shape (as well as for more general geometries) in two and three space dimensions. In an accompanying second article, we investigate the formulae in a number of numerical experiments, where we focus on the dependence of the magnetic force on the distance between the bodies and on the case when the two bodies are in contact. The aim of the analysis as well as of the numerical simulation is to contribute to the ongoing debate about which formula describes the magnetic force between macroscopic bodies best and to stimulate corresponding real-life experiments.
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