8-1

$\displaystyle \Nabla \cdot \vE$	$\displaystyle = \begin{pmatrix}\partial_{x}\\ \partial_{y}\\ \partial_{z} \end{... ...0 \end{pmatrix} =\partial_{x} \left( E_0 \cos\left(\omega t-kz\right)\right) =0$
$\displaystyle \Nabla \times \vE$	$\displaystyle = \begin{pmatrix}\partial_{x}\\ \partial_{y}\\ \partial_{z} \end{... ...ix} = \begin{pmatrix}0 \\ E_0k \sin \left(\omega t-kz\right) \\ 0 \end{pmatrix}$
$\displaystyle -\frac{1}{c}\del{\vB}{t}$	$\displaystyle =-\frac{1}{c}\deL{t} \begin{pmatrix}B_x \\ B_y \\ B_z \end{pmatri... ...t(\omega t-kz\right) \\ 0 \end{pmatrix}; \quad \because\, \omega = ck,\,E_0=B_0$
$\displaystyle \Nabla \times \vB$	$\displaystyle = \begin{pmatrix}\partial_{x}\\ \partial_{y}\\ \partial_{z} \end{... ...} =\begin{pmatrix}-B_0 k \sin \left(\omega t -kz\right) \\ 0 \\ 0 \end{pmatrix}$
$\displaystyle \frac{1}{c}\del{\vE}{t}$	$\displaystyle =\frac{1}{c}\partial_{t} \begin{pmatrix}E_x \\ E_y \\ E_z \end{pm... ...mega t-kz\right)\\ 0 \\ 0 \end{pmatrix}; \quad \because\, \omega = ck,\,E_0=B_0$