The inhomogeneous Maxwell's equations-specifically, Gauss's Law and the Ampère-Maxwell Law-are so named because they contain source terms that break their homogeneity. These sources are the charge density ( $\rho$ ) and the current density ( $J$ ), which are unified relativistically into the four-current density $K^\nu$. In the covariant formulation, these equations relate the derivatives of the electromagnetic field tensor $F^{\mu \nu}$ directly to the source four-vector $K^\nu$.
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