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Potentials and fields of a charge set suddenly from rest into uniform motion
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The fact that electromagnetic effects propagate at the speed of light suggests how the Lorenz-gauge scalar and vector potentials of a uniformly moving point charge must be modified when the charge was initially at rest and then set suddenly into uniform motion. The modified potentials are shown to satisfy the requisite inhomogeneous wave equations. The gauge function of the transformation of these potentials to the Coulomb gauge is calculated in closed form. It is validated by confirming that the Coulomb-gauge vector potential that is calculated using it yields together with the Coulomb-gauge scalar potential the same electric and magnetic fields as those calculated with the Lorenz-gauge potentials.
Forward citations
Cited by 2 Pith papers
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Novel distributional Laplacians and a Coulomb-gauge problem
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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Direct, analytic solution for the electromagnetic vector potential in any gauge
The vector potential in any gauge is expressed as the retarded potential plus a gradient built from the scalar potential, which reduces to the known gauge transformation from the Lorenz gauge.
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