Word Count : 348

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To show that the retarded scalar potential \(\phi(\vec{r},t)\) and the retarded vector potential \(\vec{A}(\vec{r},t)\) satisfy the Lorentz gauge condition, we need to verify that: \[ \nabla \cdot \vec{A} + \frac{1}{c^2} \frac{\partial \phi}{\partial t} = 0 \] --- ### Step 1: Compute \( \nabla \cdot \vec{A} \) The retarded vector potential is given by: \[ \vec{A}(\vec{r},t) = \frac{\mu_0}{4\pi} \int ____ ____ _________ _________ _________ _______ _______ ______ _______ _____ _______ __________.
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