Question

A plane electromagnetic wave of circular frequency $\omega$ propagates in free space in the direction of the unit vector $n_{1}$. Setting the wave number $\mathbf{k} = kn_{1}$ , show that

$\mathbf{k}\cdot \mathbf{E}=0, \mathbf{k}\times \mathbf{E}-\omega \mu _{0}\mathbf{H}=0$

$\mathbf{k}\cdot \mathbf{H}=0, \mathbf{k}\times \mathbf{H}+\omega \epsilon _{0}\mathbf{E}=0$

Note: $\mathbf{k}\cdot \mathbf{E}$ comes from $\bigtriangledown \cdot \mathbf{E}=0$ , and $\mathbf{k}\times \mathbf{E}-\omega \mu _{0}\mathbf{H}=0$ from Faraday's Law, etc.

Answer 1

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