Potentials of a uniformly moving point charge in the Coulomb gauge

V. Hnizdo

Potentials of a uniformly moving point charge in the Coulomb gauge

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arxiv physics/0307124 v2 pith:NBCTVZJH submitted 2003-07-24 physics.class-ph physics.gen-ph

V. Hnizdo This is my paper · ORCID

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keywords chargecoulombequationpointgaugegaugesmovingobtained

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The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector potentials in the two gauges is shown to satisfy a Poisson equation to which the inhomogeneous wave equation for this quantity can be reduced. The right-hand side of the Poisson equation involves an important but easily overlooked delta-function term that arises from a second-order partial derivative of the Coulomb potential of a point charge.

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Novel distributional Laplacians and a Coulomb-gauge problem
physics.class-ph 2025-08 conditional novelty 5.0 of 10

New distributional Laplacian identities for arsinh[a(z-b)/s] and ln[a(z-b)+sqrt(s^2+a^2(z-b)^2)] are derived and applied to solve the Coulomb-gauge Poisson equation for a uniformly moving charge.

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