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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