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The fact that electromagnetic effects propagate at the speed of lightsuggests how the Lorenz-gauge scalar and vector potentials of a uniformlymoving point charge must be modified when the charge was initially at rest andthen set suddenly into uniform motion. The modified potentials are shown tosatisfy the requisite inhomogeneous wave equations. The gauge function of thetransformation of these potentials to the Coulomb gauge is calculated in closedform. It is validated by confirming that the Coulomb-gauge vector potentialthat is calculated using it yields together with the Coulomb-gauge scalarpotential the same electric and magnetic fields as those calculated with theLorenz-gauge potentials.

Potentials and fields of a charge set suddenly from rest into uniform motion