Solution
= Solution
With $x^0=ct$, so that $\partial_0=c^{-1}\partial_t$, the $\nu=0$ component of
$\partial_\mu T^{\mu\nu}=0$ is
$$
c^{-1}\partial_t\epsilon+\partial_i(N_i/c)=0,
$$
and the $\nu=j$ component is
$$
\partial_tg_j+\partial_i\sigma_{ij}=0.
$$
These are exactly the energy and momentum conservation laws from parts (a) and (b), now combined into conservation of the electromagnetic <stress-energy tensor>.