The velocity-gauge vector potential A_2 = c∫(Phi_c - Phi^(v))dt is shown to satisfy the wave equation by four independent analytic proofs.
Direct, analytic solution for the electromagnetic vector potential in any gauge
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We derive an analytic solution for the electromagnetic vector potential in any gauge directly from Maxwell's equations for potentials for an arbitrary time-dependent charge-current distribution. No gauge condition is used in the derivation. Our solution for the vector potential has a gauge-invariant part and a gauge-dependent part. The gauge-dependent part is related to the scalar potential.
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Reply to "Comments on work of Yang and Nevels 'Direct, analytic solution for the electromagnetic vector potential in any gauge' (arXiv:2507.02104)" by Onoochin (arXiv:2507.08042)
The velocity-gauge vector potential A_2 = c∫(Phi_c - Phi^(v))dt is shown to satisfy the wave equation by four independent analytic proofs.