Notes on Electrostatics in $\mathbb R^3$

Vladimir Gol'dshtein; Wolfgang H. Müller; Reuven Segev

Notes on Electrostatics in $\mathbb R^3$

数学物理 2026-08-13 v1

作者: Vladimir Gol'dshtein , Wolfgang H. Müller , Reuven Segev

摘要

A compact formulation of electrostatics is presented. Without using constitutive relations, including the aether relations, an expression for the potential energy of a charged region under a potential function is proposed, where the charge distribution is specified by the charge potential field. Assuming that during a virtual motion of the charge, the virtual work expended by the field is equal to minus the time derivative of the potential energy, an expression for the mechanical force functional is derived. The force functional contains the action of an asymmetric active stress field D_{i}E_{j}, the skew-symmetric part of which is the mechanical couple density.

引用

@article{arxiv.2608.12900,
  title  = {Notes on Electrostatics in $\mathbb R^3$},
  author = {Vladimir Gol'dshtein and Wolfgang H. Müller and Reuven Segev},
  journal= {arXiv preprint arXiv:2608.12900},
  year   = {2026}
}