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3.7: Wave Power in a Lossy Medium
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/03%3A_Wave_Propagation_in_General_Media/3.07%3A_Wave_Power_in_a_Lossy_Medium
\[\begin{align} {\bf S}_{ave} &= \frac{1}{2} \mbox{Re} \left\{ \widetilde{\bf E} \times \widetilde{\bf H}^* \right\} \nonumber \\ &= \frac{1}{2} ~ \hat{\bf z} ~ \mbox{Re} \left\{ \frac{\left|E_0\right... $\begin{align} {\bf S}_{ave} &= \frac{1}{2} \mbox{Re} \left\{ \widetilde{\bf E} \times \widetilde{\bf H}^* \right\} \nonumber \\ &= \frac{1}{2} ~ \hat{\bf z} ~ \mbox{Re} \left\{ \frac{\left|E_0\right|^2}{\eta_c^*} e^{-2\alpha z} \right\} \nonumber \\ &= \hat{\bf z} \frac{\left|E_0\right|^2}{2} ~ \mbox{Re} \left\{ \frac{1}{\eta_c^*} \right\} e^{-2\alpha z} \label{m0133_eSave1}\end{align}$

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