On spatially-averaged electrokinetics of point charges and Maxwell's equations

Murdoch, A. Ian (2017) On spatially-averaged electrokinetics of point charges and Maxwell's equations. Journal of Elasticity. ISSN 0374-3535 (https://doi.org/10.1007/s10659-017-9647-0)

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Maxwell-like field relations which describe spatially-averaged kinematic behaviour of electrons and atomic nuclei (modelled as point charges) are obtained at any prescribed scale using weighting function methodology. Upon appeal to the experimental laws of Coulomb and Biot-Savart, and to dimensional considerations, these relations yield the macroscopic Maxwell equations as they pertain to electrostatics and magnetostatics. Generalisation to classical macroscopic electrodynamics is effected by taking account of signal transmission delay and selection of appropriate retardation potentials. Unlike previous derivations, no appeal is made to the microscopic field relations of Lorentz.