I What is the connection between the skin effect and electromagnetic waves?

[Anton Alice]

First of all, hello.
I have a problem in understanding the skin effect.
Often I read, that the skin effect is directly caused by eddy fields inside the conductor, which oppose the "desired" current flow. Problem at this is, that the eddy fields are not in phase with the desired current. The opposing current, caused by the eddy fields would be maximal, when the time-derivative of the desired current was maximal, but not the current itself. The current could be zero, while its time derivative is maximal (for example a sine).

But I also doubt my doubt:
If you look at a simple circuit with a solenoid, which is connected to a voltage supply via a switch:
-if the switch is open, nothing happens
-if the switch is closed, the inductivity of the circuit (i.e. the solenoid) responses to that singularity, which is caused by closing the switch. The response is an opposing high voltage, which inhibits the current flow in the beginning. So the current at time t=0 is zero. It is only inhibited.
Now, if I kind of apply the argument from above to this solenoid-example, I could ask myself: Why doesn't that opposing voltage create an opposing current flow? So the current at time t=0 should not only be inhibited, but also inverted.

Reality shows, that the current is not inverted, but only inhibited. And the same inhibition occurs during the skin effect. This would approve the explanation with the eddy fields.

Now I want to know, what of the above said makes sense, and eventually how the skin effect actually works?
I also have a second question:

The term skin effect is connected to "skin depth". But the term "skin depth" also occurs in relation to propagating EM-waves, which for example penetrate a conductor, and get reflected. Now I wonder, if there is a connection between skin effect and EM-waves?

 

[vanhees71]

In principle the Maxwell equations cover the full effects of em. waves. If the typical wavelength of the em. waves in a given situation is much larger than the typical extent of the matter it interacts with and you are only interested in the field close to that matter, you can use the quasistatic approximation, i.e., neglect the discplacement current in the Maxwell-Ampere-Law, simplifying it to the simpler Ampere Law. The skin effect and the penetration depth are thus of the same physics nature.

 

[Anton Alice]

Thank you for your response. Could you elaborate on that a bit more? Because I can't see the reason, why I should neglect the displacement current, if there is a non-zero time derivative of E. The fact, that E changes in time does not depend on whether I look at a wavelength scale, or macroscopic scale.

Even if you are right, I still wouldn't recognize the answer to both of my questions.

EDIT:
In the derivations I have seen sofar for the skin depth, there is no quasi-static approximation applied.

 

[vanhees71]

Sure, you can just solve the Maxwell equations with the appropriate boundary conditions. The most simple case is a conducting half-space, where you can use Cartesian coordinates. A thorough treatment is found in

A. Sommerfeld, Lectures on Theoretical Physics vol. III, Academic Press (1952)

 

[Anton Alice]

if the typical wavelength of the em. waves in a given situation is much larger than the typical extent of the matter it interacts with and you are only interested in the field close to that matter, you can use the quasistatic approximation

Does that mean, that if I am very close to a radiative source (with close I mean a distance, which is much smaller than the wavelength of radiation), I don't experience radiation?