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## Homework Statement

## Homework Equations

For a plane polarized electromagnetic wave traveling along the z axis, with its

**E**vector parallel to the x-axis and its

**H**vector parallel to the y axis, Faraday's law

[tex]\nabla\times \textbf{E}=-\frac{\partial \textbf{B}}{\partial t}[/tex]

gives that

[tex]\frac{E}{H}=\frac{\omega\mu}{k}[/tex], where E and H are the moduli of

**E**and

**H**.

ETA: It is assumed that [tex]\textbf{H}=\textbf{B}/\mu[/tex]

My problem is with an em-wave traveling in the x-z plane (were

**E**and

**k**have both x and z components). Apparently, I'm supposed to get the same ratio between E and H as above.

## The Attempt at a Solution

[tex]\begin{vmatrix}

\textbf{i} & \textbf{j} & \textbf{k}\\

ik_x & 0 & ik_z\\

E_x & 0 & E_z

\end{vmatrix}=i\omega\mu H\textbf{j} \Longrightarrow \textbf{H}=\frac{1}{\omega\mu}(k_zE_x-k_xE_z)\exp i(k_xx+k_zz-\omega t)\textbf{j}[/tex]

Taking the modulus of

**H**doesn't yield the correct answer, so I'm out of clues.

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