# I What is meant by "low frequencies"? (EM skin depth question)

1. Dec 16, 2017

### cozycoz

I'm studying conductors, where complex wave number $K=k+iα$ and complex index of refraction $N=n+iκ$ is introduced. My text book(Fowles Optics) says that for "very low frequencies", skin depth δ is equal to $δ=\frac{1}{α}=\sqrt{\frac{λ_0}{cπσμ_0}}$.
What is "very low frequency"? How much low does the frequency need to be to be labled "very low"?
In an example, the author said that the skin depth of copper($σ=5.8×10^7$mho/m) for 1mm microwaves is about $10^{-4}$mm. 1mm wavelength is equal to about $10^{12}$ angular frequency. Is this "very low"? How can I determine?

2. Dec 16, 2017

### Staff: Mentor

Compare it to the plasma frequency.

3. Dec 16, 2017

### Ibix

It's always worth a quick google. If the Wikipedia article on the skin effect is to be believed, the skin depth is your approximate formula multiplied by $\sqrt {\sqrt {1+(\rho\omega\epsilon)^2}+\rho\omega \epsilon }$. Check the references, obviously, but the necessary approximation is obvious.

4. Dec 16, 2017

Thanks...!