Potentials of a uniformly moving point charge in the Coulomb gauge
Abstract
Description
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.
To appear in European Journal of Physics. A delta-function identity for a second-order partial derivative of the Coulomb potential of a point charge is now used for the regularization of the rhs of the Poisson equation for the difference between the vector potentials in the Coulomb and Lorenz gauges
To appear in European Journal of Physics. A delta-function identity for a second-order partial derivative of the Coulomb potential of a point charge is now used for the regularization of the rhs of the Poisson equation for the difference between the vector potentials in the Coulomb and Lorenz gauges