The first of the two inhomogeneous Maxwell's equations, Gauss's Law ( $\nabla \cdot E =\rho / \epsilon_0$ ), is recovered by analyzing the $\nu=0$ (time) component of the compact relativistic tensor equation $\partial_\mu F^{\mu \nu}=\mu_0 K^\nu$. This component effectively acts as the four-dimensional temporal part of the equation, revealing the physical relationship between the divergence of the electric field ( $\nabla$. E) and the charge density ( $\rho$ ), demonstrating how the static electric field is sourced by charge.
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