Can anyone explain where the following expression for the electric field vector comes from? $$ \mathbf E(\mathbf r,t) = -\nabla \phi(\mathbf r,t) - \frac{\partial}{\partial t}\mathbf A(\mathbf r,t) $$
where $\phi$ and $\mathbf A$ are the scalar and vector potentials, respectively.
Presumably it can it be derived from Maxwell's Equations?
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