= Surface impedance of a good conductor
{title2=$Z_s=(1-i)\sqrt{\mu_0\omega/(2\sigma)}$}
For a wave penetrating a nonmagnetic good conductor in the $+z$ direction with time convention $e^{-i\omega t}$, its <wavenumber> is $k=(1+i)/\delta$, with <skin depth> $\delta=\sqrt{2/(\mu_0\sigma\omega)}$. If $\mathbf E\parallel\widehat{\mathbf x}$, <Faraday's law of induction> gives $\mathbf H=[k/(\mu_0\omega)]E_x\widehat{\mathbf y}$. Thus the field ratio is $Z_s=E_x/H_y=(1-i)/(\sigma\delta)$, equal to the displayed expression. Magnetic and electric fields have equal exponential penetration lengths but a phasor phase difference $\pi/4$; $H_y$ has the positive phase relative to $E_x$ in this convention.
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