 Solution

With $x^0=ct$, so that ${\partial }_0=c^{-1}{\partial }_t$, the $\nu =0$ component of
${\partial }_{\mu }{T}^{\mu \nu }=0$ isand the $\nu =j$ component isThese are exactly the energy and momentum conservation laws from parts (a) and (b), now combined into conservation of the electromagnetic stress-energy tensor.