# Voltage on a conductor due to skin depth

1. Mar 29, 2014

### Rahu

As we know due to skin depth effect the Alternating Current flows at a depth from the conductor surface (which means there is no voltage on the surface of the conductor, it is only at a depth from the surface).
Then how is it possible for voltage to get appeared across some other conductor which is connected to the sourcing wire (when wrapped around to tap power).

2. Mar 29, 2014

### willem2

You misunderstood the skin effect. The current density is largest at the surface.

The current density J at depth x is

$$J_s e^{-\frac {x} {d}}$$

where d is the skin depth, and $J_s$ the current density at the surface.

3. Mar 29, 2014

### davenn

and to add to what Willem2 has said, as the frequency increases the skin effect becomes more pronounced
That is ... the skin depth decreases as freq increases.
This is why it is common to find conductors in the UHF and up into microwave frequencies silver or gold plated to maximise conduction qualities of that skin zone. At microwave frequencies, the copper wire becomes nothing more that a support surface for the silver plating.

cheers
Dave

PS ... just a bit of good advice to you ....
Its really wise NOT to start a sentence with " As we all know.... "
unless you are really sure of your facts

4. Mar 29, 2014

### Baluncore

Rahu. Welcome to PF.

It takes time for a surface current flow to soak into a conductor because it sees it's own reflection.

Higher frequencies have less time to soak in before they reverse, so they penetrate less.

5. Mar 29, 2014

### davenn

not really a good description , Baluncore.
doesnt have anything to do with time taken for anything to "soak in" anywhere

try (from wiki) ....
An alternating current in a conductor produces an alternating magnetic field in and around the conductor. When the intensity of current in a conductor changes, the magnetic field also changes. The change in the magnetic field, in turn, creates an electric field which opposes the change in current intensity. This opposing electric field is called “counter-electromotive force” (back EMF). The back EMF is strongest at the center of the conductor, and forces the conducting electrons to the outside of the conductor.

cheers
Dave

Last edited: Mar 29, 2014
6. Mar 29, 2014

### Baluncore

I think I disagree with your model.
An EM wave will propagate on the surface of a conductor at close to the speed of light, 300 Mm/s.
An EM wave will propagate through a solid conductor as a wave.
The velocity through solid copper at 60 Hz is only 3.2 m/s.
The refractive index of copper in air at 60 Hz is the ratio 3x108 / 3.2 = 95 million.

What is happening now on the surface of a conductor has no immediate effect at the centre, the electric currents and magnetic fields won't get to the centre until quite a bit later, often many cycles later.

That is why I find the descriptive term “soak” so applicable to understanding skin effect.

7. Mar 30, 2014

### Staff: Mentor

There is some confusion here, so I'm closing this thread temporarily until I can sort out the technical details tomorrow.

8. Mar 31, 2014

### Staff: Mentor

Okay, I will re-open this thread now.

Baluncore -- your explanations are not accurate on this subject (you are usually correct, but this time there seems to be some misunderstanding).

The explanation at wikipedia is good:

https://en.wikipedia.org/wiki/Skin_depth

9. Mar 31, 2014

### Baluncore

Ah' such is the dominant paradigm. I apologise for my deviance.

10. Mar 31, 2014

### nsaspook

I can see his point, not all discussions of 'skin depth' are simply about electrical conductors and AC currents (like ground-penetrating radar). A better term might have been 'diffusion' instead of 'soaking' when discussing the propagation of EM waves in conductive and/or dielectric media.

Last edited: Mar 31, 2014
11. Mar 31, 2014

### Baluncore

nsaspook, thanks for the understanding. But students new to EM are too delicate to be thrown out of wikipedia and into the jungle of the real world. Wikipedia has twice ruled the day here.

12. Mar 31, 2014

### Staff: Mentor

No, sorry Baluncore. On this technical issue you have the wrong understanding of how skin depth works. There is no justifying what you posted, and no disrespecting the technical explanation at wikipedia or in our textbooks.

13. Apr 1, 2014

### meBigGuy

The wikipedia article is pretty simplistic.

A few quotes from http://fermi.la.asu.edu/w9cf/skin/skin.html (BTW the animation illustrates Baluncore's model quite nicely)

"Except for the various factors of 2i and 2$\pi$ , the skin depth is essentially the wave length in the metal. The main thing to notice are that the free space wave length is enormously larger than the skin depth."

"Notice that the skin depth being so small dominates Eq. 10, so for conductors many skin depths thick, you will always get this exponential decay as you move away from the surface. In particular you will still get this behavior even for surfaces with large radii of curvature once you are many skin depths from the surface. "

"Plots of the magnetic field and the current density are shown in figure 1. It is amusing to see that the current is not all flowing in the same direction in the conductor. From the figure, we see that there is a wave traveling and decaying into the conductor. When the current density is a maximum at the surface, the current deeper than about 1.5 skin depths is flowing in the opposite direction. The magnetic and electric fields have the same behavior. "

14. Apr 1, 2014

### nsaspook

I don't see how anyone one here is 'wrong', as usual there is more involved.

This is the important thing to remember about skin effect.
From the from wiki also.
Skin effect is not just something that happens on circular wire conductors isolated in space, it's also part of a whole system of energy transmission that uses the wiring (good conductors of many shapes) to constrain EM fields near them by reflection at a media boundary (air/vacuum <-> good conductor)

Saying the "back EMF is strongest at the center of the conductor, and forces the conducting electrons to the outside of the conductor" assumes (very simplistically) a circular solid conductor but we also see separate skin effects on the inside and outside surfaces of the shield on a coax conductor and a stripline conductor with a dielectric on one side and air on the other.

Last edited: Apr 1, 2014
15. Apr 1, 2014

### sophiecentaur

My old copy of Panosky and Philips "Classical E and M" just introduces the skin effect as the consequential reduction of the E field at depth in a conductor - a result of the boundary conditions on an incident wave. This basically applies to a wave travelling along a wire just as to a wave incident on a plane reflector. I have read the term 'evanescent mode' applied to the wave beneath the surface too.
Personal pictures / models for what's "going on" can often be misleading when presented to other people although they can work perfectly well for an individual. Maxwell's mathematical model is pretty satisfactory for most purposes, I think.

16. Apr 1, 2014

### meBigGuy

If you are going to criticize so called "personal pictures" please have the competence to describe exactly how they are misleading. I doubt you actually understand the picture or read the article I linked to. It is the result of "Maxwell's model". It illustrates the fields resulting from the effects that cause the skin effect. I challenge you to find fault with it or illustrate how it is "misleading".

17. Apr 1, 2014

### sophiecentaur

I am afraid that you are far too confrontational in your posts - not just to me and not just on this thread. It spoils a thread when personal remarks creep in. That article is, as one would expect, more or less word for word what Panofski and Philips say (without the animation) and I am not even sure what words of yours you think I was criticising.

I have an issue with words like "soaking", "back emf" and "diffusion", each of which have other connotations and can distract from message from the direct mathematical treatment. No problem when trying to make it 'easier' to approach but when trying to deal with a problem in detail, surely Maxwell is the best way to communicate and derive the relationships.

If you want to reply, please try avoid the personal angle. It really isn't necessary. Participating on PF is supposed to be a pleasant experience.

18. Apr 1, 2014

### nsaspook

In my defense "diffusion" as in diffusion equation has a specific meaning when used in relationship to EM energy movement in a conductor but maybe it is something that's not commonly used in teaching students about skin effect and energy coupling unless you need to understand EM shielding.

Electromagnetic Diffusion

Last edited: Apr 1, 2014
19. Apr 1, 2014

### sophiecentaur

I agree. Diffusion is a more applicable term than the other two terms. But does the idea go further than the straightforward field calculation that Maxwell yields in the skin depth case? I don't know enough about the diffusion approach and can't see the whole article.

20. Apr 1, 2014

### meBigGuy

@sophie
"I am not even sure what words of yours you think I was criticising."