Obtain the expressions for inhomogeneous Maxwell's equations in terms of scalar and vector potentials.

In classical electrodynamics, Maxwell's equations describe the behavior of electric and magnetic fields. The inhomogeneous Maxwell's equations can be expressed in terms of scalar and vector potentials as follows:

1. Gauss's Law for Electricity (with charge density \( \rho \)):
   \[
   \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}
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