A new principle of the theory of electromagnetic waves and conduction is formulated. It models a metallic conductor as a set of interacting neutral atoms, each consisting of a positively charged nucleus, some electrons bound to it, and free electrons. The macroscopic model of the conductor is three interpenetrating interacting continua: a positively charged set of nuclei, a negatively charged set of electrons bound to the nuclei, and a negatively charged set of free electrons (electron gas). Densities of charge carriers, partial displacements, and partial stresses are introduced. The balance equations for the densities of charge carriers, the equations of conservation of momentum, and the equations of state that relate the dynamic and kinematic parameters are derived. Based on the charge conservation equations and the Gauss–Ostrogradsky theorem, the equations of triple-continuum mechanics of the conductor are transformed into a system of coupled dynamic equations for the macroscopic displacements of the skeleton of bound charges, electric field strengths due to bound and free charges, and conduction current density. These equations are invariant under Galilean transformations. Ohm’s law and Maxwell’s equations follow from them as special cases.
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Translated from Prikladnaya Mekhanika, Vol. 56, No. 2, pp. 3–17, March–April 2020.
This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
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Khoroshun, L.P. The Triple-Continuum Mechanics of Conductors as the Basis for the Theory of Electromagnetic Waves and Conduction. Int Appl Mech 56, 127–140 (2020). https://doi.org/10.1007/s10778-020-01001-1
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DOI: https://doi.org/10.1007/s10778-020-01001-1