Skin effect theory request

[Jeroen]

I was contemplating on the skin effect.
The effect implies, that alternating, high frequency (electron) currents tend to flow on the outside(skin) of a conducting wire.
Maybe a flow of positive charged particles(deutrons) in an alternating field will tend to flow through the middle of that electric field. Unfortunately i don't understand the skin effect enough to be sure of that and internet doesn't seem to be much of a help. So if there are physicists around who can direct me to some hardcore theory i'd be really grateful.
(I hope I did make myself clear, english is not my first language)

[Richard Hull]

Any decent book on radio frequency RF engineering will fully explain the skin effect complete with equations, etc.

The skin effect in RF is for charge carrier transfer and not related to matter particles in motion in the conductor. It basically relates to metallic conductors only. Metals have the classic "sea of electrons" dangling free at the surface.

When electrical energy, or more correctly, potential different is seen along a conductor, the charges are, at the first instant, transfered only on those free charge carriers which are abundant at the surface of the metal. If all these 'easy' charges are tied up as time goes on, the current streamlines will tend to 'dive' into the metal to gain extra current carriers. If time continues and more charges require transfer, this process continues until the entire cross section of the conductor is utilized.

Direct current always utilizes the entire cross section of a conductor. Skin effect shows up even at 60 hertz in metallic conductors.

If an alternating current is applied to a metal conductor and the current flow reverses before the full current can dive into the conductor in the first alternation, the entire cross section of copper is wasted, the current is limited, and the wire looks like a resistor to AC current flow.

Tesla fought tooth and nail for 60 hertz around the late 1800s when he was assisting Westinghouse impliment his patents. Westinghouse wanted 120 hertz due to the incredibly large cost savings in transofrmer core iron and copper, not to mention the mass reduction in handling and pole strength requirements. Plus, all of Westinghouse's existing installed systems were 120hz. Tesla could see that in massive distribution systems, the skin losses would quickly outpace the savings in transformer iron. Also, much larger surface area conductors would be required on very long runs. Ultimately, Tesla's good engineering sense, looking forward to massive electrical networks, won out.

Again, the skin effect is classically viewed in metals only and relates to the nebulous "free charge carriers" (unlinked metallic surface electrons in the crystalline lattice).

You can rely on current to flow along the path of least resistance. Current is not related to the physical, motional flow of electrons AT ALL in metals. In a vacuum, ions are the only method of transport of current and may or may not, as the case may be, need to have one charged piece of matter travel with its charge from pole to pole.

i.e. In a total plasma, (arcs) current travels like in a wire. (the matter particle ions do not need to travel point A to point B to deliver the electrical energy.)

In a partial plasma or lightly ionized medium there is a mix which slowly changes to one charge delivered for one ion's full A to B motion where the mean free path allows it.

In a total vacuum of nearly infinite mean free path, ions and electrons MUST be a one for one charge carrier of each current unit A to B.

Just remember, current streamlines move along the path of least resistance. In Vacuo, with ion/electron situations, this can become highly entangled based on many, many factors. Potential differences breed current streamlines and the dv/dt relationship determines the path taken at the first instance. The abundance and location of carriers in the conducting medium will determine the instantaneous modality or path of conduction.

Wire is a very stable conducting medium. Sorta' kinda' vacuumy things with varying potentials applied are among the least understood and least diagnosable conductorish items known to man. Thus, the jokingly applied science of plasma diagnostics. This science has been used to show exactly why fusion in plasmas have failed, but not how to make them work! It is sort of a codified, mathematical Mea Culpa for upper level fusioneers.

Richard Hull

Richard Hull

[Jeroen]

Thanks Richard,

After having read that twice it was completely clear.
I thought it had something to do with a magnetic field induced by the alternating current that would positively charge the core of the conductor pushing away the electrons.(or something)
The speed and quality of this reply makes me think this is a real good forum and if I come up with another idea or problem i'll let you all know.
(p.s. didn't know you have 60hz, cause we have 50hz)

[Jeroen]

After having read that twice it was completely clear.
I thought it might have something to do with the alternating current inducing a positive magnetic field inside the conductor so the electrons would go away(or something)
Thanks for the swift and complete reply. Now i can spent my time thinking about other ways of making an inner grid out of plasma instead of metal.
If I think of someting i'll let you all know.
(p.s. I didn't know you have 60hz, cause we have 50hz)

[Jeroen]

Cause it gave an error message and still posted
over
and
over
and..

[r_c_edgar]

I deleted the rest of the repeats.

Do you remember just what the error message was?

--Ryan

[Richard Hull]

I get the same error messages all the time as well, but the message gets through anyway. I use netscape at work and explorer at home.

It says "Server encoutered internal error. Contact server administrator support@moses.com. Error information may be found in server log" ............

Richard Hull

[guest]

Ryan, that sounds like the error msg I've been getting... there's no sign that the msg has posted, but there it is.

I think it has something to do with what happens when you access the board via the link in an e-mail msg... the links in the e-mails still show "fusor.net.moses.com" as the domain, and I think that's throwing things off.... I mentioned it in an email to you and the other Ryan earlier in the week.... is is something we can sort out?

--PS

[Jeroen]

Maybe It'll show up this time as well, and you can read it in the next post

[Jeroen]

This was what i got:

Internal Server Error
The server encountered an internal error or misconfiguration and was unable to complete your request.
Please contact the server administrator, support@moses.com and inform them of the time the error occurred, and anything you might have done that may have caused the error.

More information about this error may be available in the server error log.

[guest]

Wow!!, I'm surprised there's much of a skin effect to worry about at 120Hz, is it at all related to current as well as frequency, becoming more pronounced at power station levels. I wonder if the Hall effect would be more of a problem as huge currents generate magnetic fields and force the current to the conductor surface. Hmm I'll have do some drawings on a piece of paper....how did it go again? left hand motor rule, right hand generator rule.

regards
Mark Harriss

[DaveC]

Mark - the skin depth in a homogeneous conductor is given by the following expression:
skin depth (d) = sqrt [ 2*rho/(omega* mu) ], where rho is resistivity, omega is angular frequency in radians/sec (or 2 pi freq) and mu is permeability. For copper at 60 Hz, the skin depth is approximately 8 mm, and varies inversely as the sqrt of frequency.

Conductors have a minimum AC resistance thickness which is almost exactly 1/2pi * skin depth. At this thickness, the real component of the current density (the portion in phase with conductor voltage) just becomes zero, indicating the point where the current phase has reached 90 degrees lagging. For conductors of a greater thickness than this, the interior current lags at greater than 90 degrees, and thus has a component going in oppposite phase to the conductor voltage. Thus actually reducing the net current flow, which is a bit counter-intuitive at first glance.

It can be helpful to consider a large area conductor as composed of many fine filaments each with identical resistance and self inductance, but with a mutual inductance that depends on the number of nearby filaments. For those on the exterior regions of a conductor, the mutual coupling is less than deep inside. Thus the filaments have different impedances, the deeper ones having greater reactance, and thus a larger phase lag between current and voltage.

The 60 hz AC resistance begins to make a significant effect In conductors having DC resistances of about 20 micro-ohms per foot or less - or about 500,000 circular mil cross sectional area, about 0.8 inch diameter for a stranded conductor...pretty big stuff.

At higher frequencies, the AC resistance effect becomes significant in smaller wires. AT 60 Mhz, for instance, the skin depth is about 8 microns, compared to 8 mm at 60 Hz. Thus at RF AC resistance is significant in almost all common wire sizes.

The skin effect works in a beneficial way in the high frequency fluorescent lamps, concentrating the plasma current somewhat more in the outer sheath nearest the phosphor, thus increasing the light output.

Dave Cooper

[guest]

Voltage in different countries varies considerably. Depending on what country you are in, you could have power supplied at 100V, 200V, 120V, 208V, 240V, and even a couple others. The frequency is always(?) 50HZ (like in europe) or 60Hz (like in the US). The power can be delivered with different wiring schemes as well.

In the US, we typically get 120V, 240V, or 208V. You will see a bunch of people now take me to task, saying that we get 110, 250, 115, or whatever, or that I forgot to mention 480, 13,000, and others. For the lower realms, 120V, 240V, and 208V are the correct voltages that are SUPPOSED to be supplied. Using 120V a the single-hot-wire base, you can derive 208 as 2 120V legs out phase by 120 deg (more often delivered to businesses, though that is not a hard rule). 240 is obviously 2 120V legs 180deg out of phase.

You will often hear people talk about 110, 115, 220, 250, or other voltages. This is for several reasons, the most impactful being that the power companies like to drop voltage from the traditional 120V to 115 or 110. It makes the current meters run faster...and supposedly helps out during peak periods.

P.S. 120V is actually the RMS value. The true peak value is actually around 170V.

[DaveC]

Clay is correct. There are many slightly different voltage levels in common use in the US Utilities, and quite a few more round the world.

In the USA, Utility Distribution voltages (ie: 117, 120, 234, 240, etc)... are typically set by State Public Utilities Commissions, PUC's.) Today, system efficiency concerns, result in lower line voltages, mostly to reduce the magnetizing losses in the transformers, but also to provide a small amount of load reduction, when generating and delivery capacity is strained.

Incidentally, the watt-hour meter at your power panel, is so named (Watt-Hr) because it responds ONLY the product of in-phase current and voltage (watts), integrating it over time to give watt -hrs.

Dropping line voltage a few percent, as long as one stays above 105 to 108 volts rms, will reduce the overall power consumption by an amount nearly equal to the voltage reduction. Below about 105 -108v, motors draw too much current and tend to overheat, pumps and compressors run too slowly and electro- mechanical things in general behave poorly. Many switching type electronic power supplies will run on AC input voltages from 85 -90 up to 265volts, at practically any frequency within reason

Dave Cooper