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

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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.
Original languageEnglish
Number of pages35
JournalJournal of Elasticity
Early online date30 Jun 2017
Publication statusE-pub ahead of print - 30 Jun 2017


  • macroscopic electrokinetics
  • Maxwell’s equations
  • weighting functions


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