Four-current
= Four-current
{title2=$J^\mu=(c\rho,\boldsymbol J)$}
The four-current combines charge density and <current density> into the <four-vector> $J^\mu=(c\rho,\boldsymbol J)$. With $x^\mu=(ct,\boldsymbol x)$, its <four-divergence> vanishes by the charge <continuity equation>: $\partial_\mu J^\mu=\partial_t\rho+\nabla\cdot\boldsymbol J=0$. It is the source in the covariant <Maxwell equations>.