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

In summary, the conversation discusses the concept of skin depth in conductors and its relation to complex wave numbers and indices of refraction. The textbook mentioned defines skin depth as ##δ=\frac{1}{α}=\sqrt{\frac{λ_0}{cπσμ_0}}## for "very low frequencies." The definition of "very low frequencies" is not specified, but an example is given where the skin depth of copper for 1mm microwaves is approximately ##10^{-4}##mm. The question arises whether this frequency is considered "very low" and how it compares to the plasma frequency. The conversation concludes with the suggestion to consult references and make necessary approximations for further understanding.
  • #1
cozycoz
I'm studying conductors, where complex wave number ##K=k+iα## and complex index of refraction ##N=n+iκ## is introduced. My textbook(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?
 
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  • #2
Compare it to the plasma frequency.
 
  • #3
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
mfb said:
Compare it to the plasma frequency.
Thanks...!
 

1. What does "low frequencies" refer to in terms of electromagnetic waves?

"Low frequencies" in terms of electromagnetic waves refers to the range of frequencies that have a longer wavelength and lower energy compared to higher frequencies. These frequencies typically fall in the range of 3 kHz to 300 GHz.

2. How does the skin depth of a material relate to low frequencies?

The skin depth of a material is a measure of how deeply an electromagnetic wave can penetrate into the material. For low frequencies, the skin depth is larger, meaning the wave can penetrate deeper into the material, compared to high frequencies where the skin depth is smaller.

3. Why is skin depth important for understanding low frequency electromagnetic waves?

Skin depth is important because it determines the amount of energy that is absorbed by a material when exposed to an electromagnetic wave. For low frequencies, the wave can penetrate deeper into the material, resulting in more energy being absorbed.

4. How does the conductivity of a material affect the skin depth at low frequencies?

The conductivity of a material affects the skin depth at low frequencies because it determines how easily the material can conduct electricity. A material with high conductivity will have a smaller skin depth at low frequencies, meaning the wave can penetrate less deeply into the material.

5. What are some examples of low frequency electromagnetic waves?

Some examples of low frequency electromagnetic waves include radio waves, microwaves, and infrared radiation. These waves have longer wavelengths and lower energies compared to higher frequency waves such as visible light and X-rays.

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