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## Homework Statement

A plane wave is passing through a metal. Show that the impedance Z can be given by

[tex] Z = \sqrt{ \frac{2 \omega \epsilon _0} {\sigma} } \frac{Z_0}{1-i} [/tex] where Zo is the impedance of free space and sigma is the conductivity.

You may assume that E is polarised in the x direction.

## Homework Equations

[tex] Z_0 = \sqrt{ \frac{\epsilon_r \epsilon_0}{\mu_r \mu_0}} [/tex]

[tex] E_x = E_0 e^{i(\omega t - \tilde{k} x)} [/tex]

where [tex]\tilde{k} = k - iK[/tex]

## The Attempt at a Solution

I've managed to get to the impedance in the form:

[tex] Z = \frac{ \mu_r \mu_0 \omega }{ k - iK } [/tex]

but this doesn't have any reference to the conductivity in it and I can't see how to get to the required equation from it. I thought to use [tex] \frac{\omega}{k} = \frac{c}{n} = \frac{c}{\sqrt{\epsilon_r \mu_r}} [/tex] but it didn't seem to help.