= Solution
Dot the vacuum <Ampère-Maxwell equation> with $\mathbf E$ and <Faraday's law> with $\mathbf B/\mu_0$. The vector identity
$\nabla\cdot(\mathbf E\times\mathbf B)
=\mathbf B\cdot\nabla\times\mathbf E-\mathbf E\cdot\nabla\times\mathbf B$
gives the <Poynting theorem>
$$
\partial_t\left(\frac{\epsilon_0E^2}{2}
+\frac{B^2}{2\mu_0}\right)
+\nabla\cdot\left(\frac1{\mu_0}\mathbf E\times\mathbf B\right)=0.
$$
Thus
$$
\boxed{\mathbf N=\frac1{\mu_0}\mathbf E\times\mathbf B}
$$
is the <Poynting vector>, the electromagnetic energy-flux density.
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