Home exercise 6.1.5: A field that carries no average power

$\mathrm{Re}\{-\mathrm{j}{\mathrm{e}}^{\mathrm{j}\omega t}\}=\sin \omega t$, so

$|\mathcal{P}|$ is largest, $E_0^2/{\eta }_0$, where $|\sin 2\beta z|=1$, that is at $z=-\lambda /8,-3\lambda /8,\dots$, at the instants $t=T/8,3T/8,\dots$ It changes sign every quarter period: the energy sloshes between the maxima of $|E|$ ($z=-\lambda /4,\dots$) and those of $|H|$ ($z=0,-\lambda /2,\dots$), $\lambda /4$ apart, and none of it travels on average.

The fields satisfy the boundary condition at the wall, $E_x(0)=0$. Averaging $\sin 2\omega t$ over a period gives zero, the same as $\mathrm{Re}\{{\mathcal{P}}_c\}=0$.