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I've came across the term "highly conductive lossless medium" in the context of electromagnetic waves travelling in materials.

I'm wondering how to make sense of that statement? I thought "highly conductive" implies there's energy through ohmic heating. However how can that then be a "lossless medium"?

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A good conductor is one for which $\frac{\sigma}{\omega\epsilon}\gg 1$ but a material is (nearly) lossless if the decay constant $$ \alpha=\sqrt{\frac{\omega^2\mu\epsilon}{2}} \left[\sqrt{1+\frac{\sigma^2}{\omega^2\epsilon^2}}-1\right]^{1/2} $$ is small. Ultra-low frequency electromagnetic waves propagating in rock have $\sigma\sim 10^{-3}S/m$ and $\epsilon\sim 10\epsilon_0$, yielding $$ \frac{\sigma}{\omega\epsilon}\sim 2\times 10^7 $$ and thus a good conductor while $\alpha\sim 2\times 10^{-5}$, so rock is nearly lossless at that frequency.

Note that geologists have measured such ultra low-frequency waves prior of some earthquakes.

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I don't know what the authors of the text you quote had in mind, but, for example, superconductors are both "highly conductive" and "lossless".

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