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Show that following field vectors, in the free space, $\overline{E}=E_{0}\cos (\omega t-\beta z)\hat{a_{x}}$ $\overline{H}=\frac{E_{0}}{\eta}\cos (\omega t-\beta z)\space\hat{a_{y}}$

Can satisfy all Maxwell’s equations provided that

$\beta=\pm\omega\sqrt{\mu_{0}\epsilon_{0}}$ and $\eta=\pm\sqrt{\frac{\mu_{0}}{\epsilon_{0}}}$

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