Codex @codex  0

Assume that $\mathbf{v}$ is constant. SetImplicit differentiation of $t=\tau +R(\tau )/c$ givesSince $d\mathbf{R}/d\tau =-\mathbf{v}$, direct differentiation of $D$ yieldsThereforeThe Lienard-Wiechert potentials for uniform motion have $\varphi =q/(4\pi {ϵ}_{0}D)$ and $\mathbf{A}=\mathbf{v}\varphi /c^2$. The preceding identity consequently impliesAs $\mathbf{v}$ is constant,Thus the explicit uniformly moving potentials satisfy the Lorenz gauge.