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Electron Re-arrangement and Flow in Power Lines

  1. Oct 1, 2015 #1
    I've been doing some bedtime reading in Chabay & Sherwood's Matter & Interactions textbook (https://www.amazon.com/gp/product/0470503475/) and have come across some interesting tidbits. Here they are:

    I've always pictured electrons pushing each other through a wire, kind of like peas through a drinking straw. I thought this was a good way of explaining how, for example, a ceiling light comes on immediately even though the drift speed of electrons is relatively slow. Turns out Chabay and Sherwood say it isn't so:

    c&s 755a1.jpg

    And so I think, okay, let's assume they're right. So what does the pushing? Chabay and Sherwood say it's electric fields that push the electrons through the wires, and that these fields are caused by particular, non-uniform arrangements of electrons on the surface of the wires -- electrons distinct from the "current carrying electrons" deeper inside:

    c&s 766a1.jpg

    They even ask the student to draw a map showing the arrangement of surface charges in a simple circuit:

    c&s 766d1.jpg

    And I think, Okay, that sounds reasonable. (Bear in mind that there's a lot of math between these excerpts where they make their case in a more quantitative fashion.)

    Then they explain why our ceiling light behaves as it does:

    c&s 764a1.jpg

    And that's where, I think, they fumble the ball a little. Why? Because they say, "the rearrangement of the surface charges in the circuit takes place at about the speed of light," and that "the final steady state of the circuit is established in a few nanoseconds," just before they say, "Most lighting actually uses 'alternating current,' in which case the electron sea doesn't drift continuously but merely sloshes back and forth very short distances, everywhere in the circuit, 50 or 60 times per second." Which makes me think that the "final steady state" of my ceiling-light circuit isn't so steady. The surface charges on the wires must be re-arranging themselves continuously, 50 or 60 times a second.

    In other words, it appears that the movement of electrons in a wire carrying alternative current involves both constant "re-arrangement" and "flow" like so...

    ...where the blue dots represent the "surface electrons" that move toward and away from the surface of the wire, and the pink dots represent "current electrons" that move, longitudinally, through the wire.

    Now it seems to me we can picture the various arrangements of the blue "surface electrons" in such a circuit as a forming, over time, a kind of three-dimensional sine wave in the wire, pushing the pink "current electrons" back and forth. Like so:

    At time 0 we have the wire in equilibrium. The sine wave is at 0, start of a cycle.

    At time 1 the blue electrons on the left have made it all the way to the surface, while the blue electrons at the other end of the wire have hardly moved at all. This creates a potential difference that sucks the pink electrons leftward. The sine wave has reached it's positive peak.

    At time 2 all the blue electrons have reached the surface. There is no potential difference and the pink electrons have thus stopped moving. The sine wave is again at 0, in the middle of the cycle.

    At time 3 the blue electrons on the left have fallen inward while the ones on the right are still on the surface. This creates a potential difference that pushes the pink electrons to the right. The sine wave now reaches it's negative peak.

    At time 4 all the blue electrons have fallen back to the initial state, and the pink electrons have again ceased to move. The sine wave is again at 0, end of cycle.

    Ya think?
  2. jcsd
  3. Oct 1, 2015 #2


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  4. Oct 1, 2015 #3


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    You have now discovered the truth. It has clearly come as a bit of a shock.

    You now know that an EM wave follows the wire surface.
    That the electron disturbance travels on the surface of the conductor at close to the speed of light.
    The conductive wires guide the E and M fields that carry energy from the supply to the load.
    The direction of the energy transfer is the Poynting vector.
    The electric and magnetic fields between the wires carry the energy, not the wire.
  5. Oct 1, 2015 #4
    In Standard Handbook for Electrical Engineers we read
    "The usually accepted view that the conductor current produces the magnetic field surrounding it must be displaced by the more appropriate one that the electromagnetic field surrounding the conductor produces, through a small drain on the energy supply, the current in the conductor.
    Although the value of the latter may be used in computing the transmitted energy, one should clearly recognize that physically this current produces only a loss and in no way has a direct part in the phenomenon of power transmission."
  6. Oct 1, 2015 #5
    Yes, thank you. More below.

    See below.

    The place where Chabay and Sherwood helpfully elaborate on the above statements (and the part that I've personally found enlightening) is where they describe the physical mechanism that causes the various fields that move the "current electrons" through the wire; they describe a physical mechanism that is definitely in (or at least on) the wire (and thus somewhat immune to the particular configuration of the wire, which has concerned me for some time); specifically, they attribute the fields to the non-uniform surplus/deficit of electrons on or near the surface of the wire in various places. In other words, the fields, in the Chabay and Sherwood model, are an effect (of electron re-arrangement) first, and only afterward the cause of further activity (current flow). Three observations:

    1. I think the Chabay and Sherwood model is helpful since it answers "troublesome" questions that students often and naturally raise -- questions not typically addressed in standard texts. For example, many students intuitively insist, even when they're told that the current flow on both sides of (and inside) a resistor is the same, that there must still be something different in the wires before and after the resistor; that electrons must, in some way, "pile up" on the one side: and Chabay and Sherwood give them a satisfying answer -- electrons do indeed "pile up" on one side and not the other; there's a significant difference in surface charge on the two sides.

    2. The Chabay and Sherwood model is also helpful because it makes it clear that we're dealing with two distinct roles for electrons in a circuit: (a) the electrons involved in the generation of the various fields along the wires (the ones I've colored blue) and, (b) the electrons involved in current flow (the pink ones). I find this distinction helpful because, while the "I" in V=IR has always had a easy-to-understand relationship with electrons (6x10^18 "pinkies" past a point per second), the "V" has only been described using abstract terms like pressure and potential. "V", in the Chabay and Sherwood model, is a much more tangible thing -- a measure directly related to the difference in the number of "blue" electrons on or near the surface of the wires and devices in two places. In short, thanks to Chabay and Sherwood, we can now understand (and picture) both current and voltage in terms of the arrangement/movement of electrons. In an earlier thread I posted this picture, describing what I intuitively thought must be happening in the wires between a guitar pickup and an input resistor:

    pickup circuit 4.jpg

    Turns out that intuitive guess wasn't far off, at least according to Chabay and Sherwood (though the ratio of surface-to-current electrons is a bit exaggerated in the images -- seems it doesn't take many surface charge electrons to move a lot of current electrons). At t1 there really is an excess of electrons on the (surface of) the bottom leg of the circuit, and a corresponding deficit of electrons on the (surface of) the top leg. And at t2 there really is a dearth of electrons on the (surface of) the bottom leg, with a corresponding surplus on the top leg. We thus have a picture that agrees with the words that agrees with the formulas; intuition and reality have kissed.

    3. In spite of how helpful the Chabay and Sherwood model is, it in essence only moves the big question back a step. What causes the surface electrons (the blue ones) to behave as they do? How do they "know" to pile up here rather than there? How do they all "get the message" so quickly? Obviously they must interact with each other in some way and/or be operated upon by some outside force. What are those interactions and/or forces at play? Ah, the "scientific method" at work -- with each answer comes more questions!
  7. Oct 1, 2015 #6


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    I think you maybe have started accepting information that's been told to you at least a hundred times in the past. If the fog has lifted you can now see now how wonderfully consistent and simple in principle the truth is.
  8. Oct 1, 2015 #7
    Slow learner, I guess. I thank all who have been patient with me.
  9. Oct 1, 2015 #8


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    I think your OP misses some key points that are explained in the skin effects article linked above.

    The "pink" electrons in the center hardly move at all. It is the electrons at the skin that carry the power current. The approximate electrical model of a solid wire with AC is that of a hollow cylinder.

    Distribution of current flow in a cylindrical conductor, shown in cross section. For alternating current, most (63%) of the electric current flows between the surface and the skin depth, δ, which depends on the frequency of the current and the electrical and magnetic properties of the conductor.

    Your analysis based on charge density is seriously deficient because it does not consider the dominant effect, namely eddy current loops.

    Skin depth is due to the circulating eddy currents(arising from a changing H field) cancelling the current flow in the center of a conductor and reinforcing it in the skin.

    Skin effect is why power line conductors (and common lamp cords and even cheap USB cables ) are multi-strand. For one thing, a multi-strand bundle has a higher ratio of surface area/mass than does a solid wire. For another, each conducting strand in the bundle carries current, even the ones that pass through the center of the bundle. Some power line conductors have a center core that is selected for tensile strength, not electrical conductivity. The spiral twisting of the strands also aids the electrical properties although I don't remember how. Busbars designed for extremely high currents are actually built as hollow cylinders.


    The same reasoning applied when there are multiple conductors per phase in high voltage power transmission lines, 2, 3, and even 4 multi-strand bundles are strung. They are always arranged as if on the perimeter of an imaginary circle. None are routed through the center of the circle. That is illustrated by the spacer below which can arrange 6 conductors in a single phase of a three phase line. The bottom picture shows four conductors per phase. The multiple conductors approximate the electrical characteristics of a large-diameter hollow cylinder which gives less losses than the same mass of strands all wound on a single bundle with a smaller diameter and much better than the same mass as a solid wire.


    All this arrangement of strands, bundles, and conductors is designed to minimze the resistive losses of the power line.

    Edit: I neglected to say that each strand in a multi-strand bundle has its own skin effect, and that small-diameter eddy-current-loops have less losses than large-diameter loops. The extremely fine strands in a lamp cord bundle have relatively little eddy current losses.
    Last edited: Oct 1, 2015
  10. Oct 1, 2015 #9
    It appears my previous drawings have been misleading -- the pink electrons are not literally "in the center" of the wires, they are just further in than the blue surface charge electrons that generate the fields that move the pink ones. No doubt the entire "electron sea" is closer to the surface than the center; after all, a copper pipe (with nothing but air in the center) makes a fine conductor.

    But according to Chabay and Sherwood, the electrons in this close-to-the-surface sea divide into two groups, each serving a distinct purpose: (a) the members of the blue group positioning themselves, at the speed of light, non-uniformly on the surface of the conductors and thus creating potential differences which in turn create electric fields that move (b) the members of the pink group through the wire at much slower speeds -- also near the surface, no doubt, but further in than the surface charges. Here's a better rendition of my previous image:

    powerline 6.jpg
    The arrows show electron flow, not conventional current. Note that it's the pink electrons that constitute the bulk (if not all) of the current; the blue electrons move mostly (if not only) toward and away from the surface of the wire to create the necessary fields to move the pink ones. Seems to me this is consistent with your illustration of eddy currents above (albeit with a minor change in coloring to separate the two groups, and a slight re-arrangement of the pink arrows to make it clear that they, too, are near the surface):

    powerline 7.jpg

  11. Oct 1, 2015 #10


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    Better yes, but you still don't acknowledge the circular loops of the eddy currents. Some electrons move opposite to the current flow some of the time.
  12. Oct 1, 2015 #11


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    The movement of electrons is largely random and thermal - more or less 50% 50% forward and backwards. The net movement is a very small proportion of the electrons and that's what constitutes the current that's measured.
  13. Oct 1, 2015 #12


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    The magnetic fields are still shown inside the conductor. Only about 1 part in a million is inside the good conductor, the rest of the field is outside with the current flowing in the surface skin.

    The surface of a good conductor is a very good mirror to EM fields. The incident magnetic field at the surface induces a current on the surface at right angles. That eddy current again generates a magnetic field at right angles, which is then the opposite direction to the incident wave, 90° + 90° = 180°. They cancel with very little loss, hence the mirror.

    But the small amount of current and magnetic field that does penetrate the conductor represent the resistive loss of the conductor. The more resistive the material, the deeper the diffusion into the material and the greater the “resistive losses”.

    So any electrons that diffuse into the wire due to imperfect conduction represent loss. Any electrons that remain on the surface represent efficient support for the conduction of energy.

    That is a quite different model to the junior guide to electricity, where the current flows in the wire, while the magnetic field radiated represents a loss of energy.
    Once you reverse that early concept, you have begun the exciting transition to become an electro-magnetician.
  14. Oct 1, 2015 #13
    I do acknowledge them. In fact, I'm picturing the blue dots in this diagram...

    powerline 6.jpg
    ...moving like the blue arrows in this diagram:

    powerline 7.jpg
    It's just hard to show at the smaller scale. It seems to me that the smaller eddy currents are undesirable and that in the ideal (but, I imagine, impossible-to-achieve) case the blue guys would simply move toward and away from the surface of the wire, as required, and may also follow the path of the larger blue loops (which seems harmless enough, and may even prove beneficial). But in this ideal case they would avoid the smaller blue loops which actually oppose the pink flow of current about half the time.
  15. Oct 1, 2015 #14
    Yes, I believe that is what Chabay and Sherwood and I are saying. Non-uniform accumulations of blue surface electrons create the fields that move the pink current electrons that are further (but not very much further) inside the wire.
  16. Oct 1, 2015 #15


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  17. Oct 1, 2015 #16


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    Thank you Baluncore. That was very helpful. It helped me expand my horizons. It would make a great PF Insights article.
  18. Oct 1, 2015 #17
    I saw those diagrams when I was first looking into this matter and found them somewhat hard to take at face value. Apparently Chabay and Sherwood had a similar reaction since they begin their discussion with these questions:

    c&s fields 1.jpg

    Their final answer is that while it is true that the fields in and around the wires move the "current electrons" in a circuit, it is the arrangement of surface electrons that determines the fields, and thus the flow of electricity. As we know from experience, this flow is more-or-less immune to changes in the physical configuration of the wires (at reasonably low frequencies) since the surface electrons automatically re-arrange themselves, at the speed of light, to compensate for layout changes. This, in fact, was the question that puzzled me at the beginning: If the energy in a circuit is carried by the fields, as indicated in a drawing like this...

    fields 1.jpg

    ...then why doesn't a significant change in physical configuration make the bulb more or less bright? Or, as I originally asked, why doesn't the physical configuration of the heater wires in a tube amp, like those variants shown below, have a greater effect on performance?

    guitar amp layouts.jpg

    (The bottom right layout uses the chassis as one of the wires.) Thanks to Chabay and Sherwood, the answer is now clear: the surface electrons arrange themselves differently in each case to automatically compensate, as best they can, for variations in the layout. In short, the surface electrons automatically arrange themselves so that the resulting fields will normalize the flow of current electrons in the circuit.
  19. Oct 1, 2015 #18


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    Yes. But it would need to include the deeper skin effect reverse currents that cancel. I have considered it, but best for now is to exercise the ideas in threads like this until we can get a good clean modular framework of understanding.

    Where the conductors fold back to lessen the distance, the electric field remains the same voltage while the magnetic field of the overlap mostly cancels. That shortens the circuit electromagnetically, in the same way as using shorter wires. It is often forgotten that the voltage drop along the wires is much less than the drop across the load.

    The external fields create the surface currents as the fields are guided by the surface current formation. The wire is like the hand rail on stairs. As the wave travels, it runs it's hand along the conductor, coordinating the movement of surface electrons in the process. The electron current is a proxy for, and an artefact of, the guided magnetic field.
  20. Oct 2, 2015 #19
    Okay, but back up one step. What creates the external fields?
  21. Oct 2, 2015 #20


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    The return circuit of two wires to the load is actually a parallel transmission line. When you connect the battery the voltage step needs to charge the capacitance of the source end of the T'line. The charge that begins to flow through the source creates the first magnetic field. That voltage step transient flows out and along both the lines toward the load followed by the magnetic field and induced surface current.

    It is easy to get into a chicken or egg situation if you look at the wire only. But making the circuit between the voltage source and the transmission line demonstrates clearly that the energy flows out of both the top and bottom of the battery as one EM wave.
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