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Electrodynamics from the viewpoint of modern continuum theory—A review

Müller, Wolfgang H.; Vilchevskaya, Elena N.; Eremeyev, Victor A.

This paper wants to draw attention to several issues in electrodynamic field theory and to make way for a rational continuum approach to the subject. The starting point are the balances for magnetic flux and electric charge, both in a very general formulation for volumes and for open surfaces, all of which can deform and be immaterial or material. The spatial point‐of‐view for the description of fields is favored and its advantages in comparison to the concept of material particles is explained. A straightforward answer to the question of how to choose units for the electromagnetic fields most suitably is also presented. The transformation properties of the electromagnetic fields are addressed by rewriting the balances in space–time notation. Special attention is paid to the connection between the two sets of electromagnetic fields through the so‐called Maxwell–Lorentz–æther relations. The paper ends with an outlook into constitutive theory of matter under the influence of electromagnetic fields and a discussion on curious developments in context with Maxwell's equations.
Published in: ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 10.1002/zamm.202200179, Wiley