Charge densities that change linearly with time are effectively electrostatic
Classical Physics
2018-01-01 v2
Abstract
We consider classical electromagnetic systems in which the current density does not change with time, but has nonzero divergence, so that electric charge does build up steadily over time. We show that for such a system, the \emph{exact} electromagnetic fields are given by the Coulomb and Biot-Savart laws with the sources evaluated at the \emph{present} (rather than retarded) time, even though the charge density is changing over time.
Cite
@article{arxiv.1708.05060,
title = {Charge densities that change linearly with time are effectively electrostatic},
author = {Edward Parker},
journal= {arXiv preprint arXiv:1708.05060},
year = {2018}
}
Comments
After posting this article, I discovered that its result was already reported in Griffiths and Heald, Am. J. Phys. 59, 111 (1991)