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Questions on electron transport in metals

Discussion in 'Electronic Basics' started by Peter, Dec 16, 2004.

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  1. Peter

    Peter Guest

    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]


    2. 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"?


    3. 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?


    4. 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?


    5. 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?


    6. 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?


    7. 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
     
  2. Guest

    This paper answers several of your questions:


    A unified treatment of electrostatics and circuits
    Sherwood & Chabay
    http://www4.ncsu.edu/~rwchabay/mi/circuit.pdf


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

    Peter Guest

    Thank you so much for the reference.

    Peter
     
  4. Guest

    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.

    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.

    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/
     
  5. Bob Masta

    Bob Masta Guest

    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
    www.daqarta.com
     
  6. John Larkin

    John Larkin Guest


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

    John
     
  7. John Fields

    John Fields Guest

     
  8. Mike

    Mike Guest

    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
     
  9. John Larkin

    John Larkin Guest

    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
     
  10. Mike

    Mike Guest

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

    Franz
     
  12. Not quite instantly.
    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?
     
  13. John Larkin

    John Larkin Guest

    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
     
  14. Doug

    Doug Guest

    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
     
  15. Androcles

    Androcles Guest

    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
     
  16. Bob Masta

    Bob Masta Guest

    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
    www.daqarta.com
     
  17. Guest

    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.
     
  18. Guest

    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.
     
  19. Guest

    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.
     
  20. Mike

    Mike Guest

    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
     
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