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Questions on electron transport in metals

Hello:

I have a couple of questions on electron transport (in metals):

  1. Consider a metal wire connecting the two terminals of a power source. What exactly happens? Is it correct to say that electrons behave as particles and flow in the wire at the drift velocity (v) amidst random thermal motion to produce the required current? [I = n*(-e)*v*A; I: current, n: free electron density, e: electronic charge, A: cross section of the wire]

  1. What exactly "makes" the electrons to flow? If it is the electric field, what causes the electric field? Would it be correct to say that the electrons at one end of the terminal have a higher ionization potential compared to the other end and that the electric field is just a convenient way to express this difference in the "potential energy"?

  2. Don't electrons themselves, being charged particles, create an electric field? Shouldn't the electrons so rearrange themselves to counteract this external field and so stop the flow of current?

  1. Does one terminal keep supplying electrons steadily into the wire to prevent the stagnation of current as mention in Q3 above? If so, is there a concentration gradient of electrons along the wire from the source terminal to the drain terminal?

  2. What happens if there is a bend in the wire? Shouldn't that affect the field created by the electrons? Shouldn't it affect the current flow? In other words will the following two structures have the same resistance (assume they have the same total length):

S________________D

S____/\\______D S: Source , D: Drain

What, in particular, if the wire dimensions are comparable to the electron mean free path?

  1. I know that the energy of the electron in a metal (or in any periodic lattice) is related to its momentum through the band structure. How does this actually affect the particle picture of electron flow in a metallic wire?

  1. I know that, for low electric fields, wave packets of electrons in a band can be considered to behave as particles obeying Newtons laws to describe the time dependence of their (crystal) momentum. Please correct me if my understanding is incorrect/incomplete. Any answers to enlighten me will be sincerely appreciated.

Peter

Reply to
Peter
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This paper answers several of your questions:

A unified treatment of electrostatics and circuits Sherwood & Chabay

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((((((((((((((((((((((( ( ( (o) ) ) ))))))))))))))))))))))) William J. Beaty Research Engineer snipped-for-privacy@chem.washington.edu UW Chem Dept, Bagley Hall RM74 snipped-for-privacy@eskimo.com Box 351700, Seattle, WA 98195-1700 ph206-543-6195 http//staff.washington.edu/wbeaty/

Reply to
billb

Thank you so much for the reference.

Peter

Reply to
Peter

In other words, "Why does a battery produce a potential difference," or "why does a generator produce a potential difference," or "why does a solar cell produce a potential difference," or ...

The answer is different for each. The reason for the e-field depends on the type of energy source.

just

energy"?

Yes, a few electrons at one end of the wire were originally in a low- energy state, and these electrons were removed. Electrons in a high- energy state are placed at the other end of the wire. In some respects the long copper wire behaves as a single gigantic atom: electrons in a high-energy location will travel to a low-energy location, emitting phonons as they do (and the wire becomes warm.)

Correct. The current exists in the wire BECAUSE the electrons are trying to rearrange themselves. But no matter what the electrons do, there is a charge-pump device which scoops electrons out of one end of the wire, pushes them up into a higher-energy state, and deposits them into the other end of the wire.

to

Yes and yes. But note that, since electrons repel each other, they will all move slightly in order to force the "region of electron- imbalance" outwards. The electron-excess at the negative-charged end of the wire will be found on the surface of the metal. The same is true of the electron-deficeit on the positive-charged end.

Yes, this is a major issue. It is treated in the paper I referenced in my earlier message.

In nano-sized semiconductors and in macro-sized vacuum tubes the mean free path is long. The usual "circuit rules" break down in both these situations. The electrons in a Klystron or in a CRT behave very differently than in a resistor. The same is true of "ballistic transistors."

Except for explaining how resistors work, this issue is mostly ignored in circuitry explanations. The velocity of electrons during an electric current is very low (they move like a clock's minute-hand!)

The energy which is being transferred by electric circuits is not transferred by electrons, instead it is stored in the EM fields surrounding the wires, and it does not travel within the metal. There *is* some EM energy-flow within the metal, but it is directed radially inwards as the external EM fields lose a bit of energy and the metal is heated.

((((((((((((((((((((((( ( ( (o) ) ) ))))))))))))))))))))))) William J. Beaty Research Engineer beaty(a)chem.washington.edu UW Chem Dept, Bagley Hall RM74 billb(a)eskimo.com Box 351700, Seattle, WA 98195-1700 ph206-543-6195 http//staff.washington.edu/wbeaty/

Reply to
billb

Not instantly, but at the speed of sound in marbles. Just like the speed of light for electrons.

John

Reply to
John Larkin

ignored

Did you try that? Your intiition fails when the marbles get stuck. You need a lot of lubrication to perform you 'intuitive' analogy for long pipes. In contrast, while resistance of wires may increase depending on dimensions, there is always a finite current flowing and electrons never get 'stuck'. Thus, your analogy is false. It has no connection whatsover to current generation and flowing, a phenomenon that its causes are still subject to hypothesis whilst its effects are detected experimentally.

Mike

Reply to
Mike

The "signal", a sudden push at the inlet side of the pipe, can't reach the output end any faster than the speed of sound in the medium. A compression wave flows down the pipe and zots the last marble out. For electrons in a wire in free space, the compression wave flows at c.

Of course, a smooth steady slow flow of marbles will have a uniform steady-state velocity, just like a steady current moves carriers slowly.

When NASA first tested the Saturn S1B booster rocket, they instrumented it with tons of accelerometers and fast telemetry. They were surprised at first when they fired the main engines and discovered that the bottom of the rocket accelerated right away, but the top lagged behind. It took a measurable amount of time for the force to propagate up the structure at the speed of sound (speed of sound in the complex structure, of course.)

John

Reply to
John Larkin 

--
I don\'t think so. The speed of the marble leaving the far end of the
pipe will be the same as the speed of the marble going into the pipe,
which can be subsonic, supersonic, or whatever.  With C as the limit,
of course. :-)
Reply to
John Fields

pipe,

limit,

reach

For

No, that's a different situation. The delay is due to the non-rigidity of the rocker composition, or any large structure for that purpose which can be modelled in an approximate way by a complex arrangement of spring-mass-damper systems. The delay in this case is due to the time constants of those second order dynamical systems.

In the case of the electrons moving in a wire the time constant delay is due to capacitance and inductance of the wire resulting in 2nd order dynamics also.

Engineers were introduced to the 'analogies' in 70-80's in an attempt to provide a unified way of modelling dynamical systems, whether electrical, mechanical or hydraulic. However the physics behind each of those systems are very different and any reference to analogies beyond the concept of a 'model' are inappropriate IMO.

Mike

Reply to
Mike

That speed will, I think, be lower than the speed of sound in an equivalent solid cylinder of glass. The marbles only touch at small places, so the coupling is low. Dispersion will be terrible because of the many random-ish paths (unless they're nicely lined up) so the pressure pulse at the outlet will be very sloppy. The waveform should be interesting.

John

Reply to
John Larkin

A good intuitive example is a pipe full of marbles. If you push another marble into one end, a marble on the far end moves out "instantly", even though it is a long way away.

Best regards,

Bob Masta dqatechATdaqartaDOTcom D A Q A R T A Data AcQuisition And Real-Time Analysis

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Reply to
Bob Masta

Speed of sound in various solids in m/s from a web stie. I made no attempt to confirm

Diamond 12000 Pyrex glass 5640 Iron 5130 Aluminum 5100 Brass 4700 Copper 3560 Gold 3240 Lucite 2680 Lead 1322 Rubber 1600

Reply to
Doug
[snip]

Not quite instantly. The pressure you apply at the input end is propagated at the speed of sound in the marble column

Franz

Reply to
Franz Heymann

It is? This seems very un-intuitive to me. Dont know why, it just seems wrong. Sure, sound is vibration in a medium (?) so it kind-of makes sense. I guess the speed of sound in very hard materials is very high?

--
John Bäckstrand
Reply to
John Bäckstran

"John Bäckstrand" wrote in message news: snipped-for-privacy@spamgourmet.com...

Yep.

This seems very un-intuitive to me.

Can't think why. If you hit one end of a rubber rod with a hammer will the other end move instantaneously? Androcles.

Dont know why, it just seems

Reply to
Androcles

Androcles wrote: If you hit one end of a rubber rod with a hammer

No. The information propagates at the speed of sound, as others have said. It is the same physical process as sound transmission: adjacent atoms colliding or exerting force on each other.

As for electric signals, they propagate at the speed of light in the medium. For a typical BNC cable, it's about 2/3 times c.

Reply to
redbelly98

Probably right about the speed of sound being lower than for a solid object. But, random paths don't necessarily make for sloppy waveforms. Sound travels through randomized collections of molecules (like air) just fine, as people are able to speak and hear each other clearly.

Reply to
redbelly98

Mike, it was an *intuitive* example, just to get across the concept that the speed of information (energy) travel can be much faster than the speed of the individual carriers. In that respect it is a very good analogy, because the reasons in both cases are the same: Each marble pushes on the one ahead of it, and the force is transmitted "instantly". (I used quotes to avoid getting into the speed of sound issue.)

To demonstrate this to kids, I use a piece of PVC about a foot long, filled with black marbles. A long rubber band runs from end to end and holds in the marbles. When you push a marble in one end, you have to overcome the resistance of the rubber. That aspect may have no particular analog, but it cause the marble on the far end to "pop" out of the pipe like magic. When kids first see this, it fits with the idea that electricity is instantaneous. I repeat this a few times until they expect to always see a black marble pop out, but I've secretly put a white marble a few positions down the pipe. So when they see a black marble go in and a white marble pop out, they "get" the idea that it's not the *same* marble coming out. That's a very important concept, and leads to a discussion of the amazing fact that they could *walk* faster than the electrons move in most ordinary situations. They can understand that after understanding the pipe analogy.

Best regards,

Bob Masta dqatechATdaqartaDOTcom D A Q A R T A Data AcQuisition And Real-Time Analysis

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Reply to
Bob Masta

You

Simply use frictionless marbles in your thought-experiment.

Or, build a 20cm version, then pretend that no new effects will arise when applied to a 20KM version.

Your argument is fallacious. If you try to prove that a model is not an model, by showing that it's imperfect... instead you have only proved that it's NOTHING BUT a model!

By definition, a model is different than the real-world phenomenon being modeled. If in the situation where the model is used, the differences are irrelevant, then the model works well.

If you don't like the "marbles" analogy, here is how to defeat it. First look at the purpose of the model: to explain electric circuits to children in a simple way. Then find places in which the model fails at its task. If the "marbles" analogy gives more misconceptions to children than it gives them understanding, then the "marbles" model fails, and nobody should use it.

But if the model gives them major insights, yet gives little or no misconceptions, then the model is EXCELLENT, and all its imperfections are irrelevant.

On the other hand, if the same "marbles" analogy was being used to teach physics grad students about the details of quantum mechanics of metals, then it would be a bad model.

Yes. Your point? Sound is not an EM wave. That's what "analogy" means.

Reply to
billb

You

long

on

detected

Bob, I understand your point but my point is that at the end of the day this type of analogies have an adverse effect in the minds of those people, the majority that is, who do not understand the purpose of modelling. It has the potential to create ellusive connections in the minds of people and eventually turn them into cranks.

I insist this whole approach is wrong although well motivated. There are discussions going on on this recently and the need to change the whole approach to teaching physics.

The model you described is problematic, I think highly. It does not demonstrate how 'information' travels faster than individual carriers. Simply because there is no indication in your example what kind of information is transmitted. The information cannot be the carrier itself. If you try to actually transmit information, you will find out that dynamics enter into the picture and analogies start failing. As an example, ask a student to paint the incoming ball a color of his choice. What color is the ball coming out the other way? If it's not the same, the information was not transmitted faster than the speed of individual carriers but exactly at the speed of those carriers, as you will have to push in several balls until you get the collor one out. Mike

Reply to
Mike

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