Charge densities that change linearly with time are effectively electrostatic

2017/07/18 by Edward Parker, Parker, Edward
Chemistry · Physics and Astronomy · #Classical Physics (physics.class-ph) #Electrostatics and Colloid Interactions #FOS: Physical sciences #Force Microscopy Techniques and Applications #Spectroscopy and Quantum Chemical Studies #physics.class-ph

paper · pdf · doi:10.48550/arxiv.1708.05060

After posting this article, I discovered that its result was already reported in Griffiths and Heald, Am. J. Phys. 59, 111 (1991)

openalex publication_date 2017/07/18 · arxiv created 2017/12/29 · arxiv updated 2018/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider classical electromagnetic systems in which the current density \bf J 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 exact electromagnetic fields are given by the Coulomb and Biot-Savart laws with the sources evaluated at the present (rather than retarded) time, even though the charge density is changing over time.

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