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Some reflections on electromagnetic force in matter

This contribution revisits different electromagnetic stress tensor concepts in matter and points out that the Lorentz force - or better the ponderomotive force in matter - is not unique, but depends on the chosen stress tensor concept. In particular, the pictures of Maxwell, Minkowski, and Einstein & Laub are reviewed, all resulting in different formulae of volume-distributed forces. Caution has thus to be paid when dealing with force calculation results if the chosen concept is not clearly declared. Furthermore, it is figured out that these forces cannot be used in a simple deformation calculation considering only the material's elasticity. In the general case, effects of magnetostriction or electrostriction have to be taken into account. A general conclusion of this paper is that there exist no sharp separation line between the electromagnetic and mechanical domains. When dealing with material constitutive equations, it is recommended to use the total stress tensor as this tensor is invariant against the choice of the electromagnetic concept.