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The Field Model of Energy Transfer in Actual Circuits

  1. Aug 9, 2015 #1
    In this paper (http://science.uniserve.edu.au/school/curric/stage6/phys/stw2002/sefton.pdf) the author describes the transfer of energy in an electrical circuit as follows:

    "To explain energy transfer we need to look at what is happening outside the wires. As a consequence of the surface charges on the wires, there is an electric field in the space outside the wires (as well as inside). Also, as a consequence of having a current in the wires, there is a magnetic field in the space around the wires. It is this combination of electric field and magnetic field in the space outside the wires that carries the energy from [source] to [load]. Once the fields are set up, the energy travels through space, perpendicular to both the electric field and the magnetic field, at the speed of light."

    I've read similar descriptions in a number of places, often accompanied by a diagram showing the various fields that are participating in this energy transfer, like this:

    fields 1.jpg

    Now here are four photos of alternative layouts for the filament wiring in vacuum-tube amplifiers:

    guitar amp layouts.jpg

    (The bottom right amplifier uses the chassis as one of the conductors in the filament circuit.) The total current carried by these wires is typically 2 to 3 amps, and the voltage (most often AC, but sometimes DC) is usually 6.3 volts. A similar variety of layouts can be found in the high-voltage portions of such circuits as well.

    Now based on the diagram above, I would think the electric and magnetic fields in these various configurations would be significantly different. As different, perhaps, as the diagram above and, say, this one:

    fields 2.jpg

    And yet I've found (in spite of the claims of various aficionados) no significant subjective difference in the performance of such widely different layouts; and certainly no objective difference in the voltage and amperage readings at the corresponding spots. Sure, we might get a little more or less hum one way or another (though, in practice, that's not as easy to predict as one might think); but we never see a significant change in the voltage or current based on the layout.

    In other words, it seems to me that while these various fields may be truly present as described, it's hard for me to imagine that they are the primary conduit for the transfer of energy in such circuits. Seems to me that the energy is being transferred through the actual conductors (wires or chassis or both), not via the space surrounding those conductors.


    Last edited: Aug 9, 2015
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  3. Aug 9, 2015 #2


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    If you calculate the fields in the last layout in detail, you'll get the same result as for the first diagram. The calculation is just much more complicated - a good argument why circuit analyses are always done with voltages and current flows in the conductors unless the circuit is designed for really high frequencies.
  4. Aug 9, 2015 #3


    Staff: Mentor

    Why is that hard for you to imagine? Also, why does it matter?

    How would you make an experiment to determine that? For example, have you even calculated how quickly the energy flux falls off outside of the wire to give you an idea of the spatial scales you have to investigate? Do you have a method for measuring energy flux that you could use inside and outside?
  5. Aug 9, 2015 #4
    I don't know about that because I don't know how to do the calculation (and haven't seen it done by anyone else). But I find it hard to believe that the size and shape of the fields are identical when in one case the wires are narrow and twisted around each other, and in another the entire chassis is employed as one of the conductors.

    I do know that the theoretical intent behind twisting the wires (top left layout) is to neutralize those fields in the interest of minimizing hum -- and yet these supposedly neutralized fields somehow manage to transport the same amount of energy to the filaments!

    It matters because I'm trying to understand what the author is saying. If, as he suggests, the energy transfer is via the fields (and not the wires), and if the fields are by definition sensitive to the relative sizes, lengths, and positions of the wires, then the performance of the circuit should be equally sensitive to changes in those sizes, lengths, and positions. This has not been the case in my (admittedly limited but apparently relevant) experience: thus, it is "hard for me to imagine."

    The "experiment" -- crude though it may be -- is as I've described it. If the primary conduit for energy transfer is the fields and not the wires, then the energy transfer (ie, the power, the volts and amps that reach the filaments) should be more sensitive to the circuit layout than they appear to be. Surely the size and shape of the fields around a twisted pair of wires is different than the size and shape of the net field around a single wire plus a whole chassis? But I could, of course, be quite wrong: it's admittedly a "smell test" and not a rigorous examination at microscopic scales.

    Here's another experiment we can perform easily enough. If you could roughly sketch out in bright colors -- or even describe in words -- the size and shape of the electric and magnetic fields in the four cases shown in black-and-white below, I think that would go a long way toward showing me how the difference in layout does not greatly affect the size and shape of those fields and thus does not greatly affect the transfer of energy via those fields.

    guitar amp layouts 2.jpg

    Perhaps this will help. When I read practical engineering texts -- whether about filament windings or transmission cables -- I get the distinct impression that these fields around the wires are essentially unwanted side effects that we should strive to minimize (unless, of course, we're building an antenna); on the other hand, the physicist (like the above author) appears to be telling me that these fields are the essential and primary means of energy transfer. Can you see how this might confuse a beginner like me?
    Last edited: Aug 9, 2015
  6. Aug 9, 2015 #5
    If you consider wires to be wave guides, this might make more sense. Use the Poynting Vector: S=ExH.

    BTW, there is a measurable difference between the twisted path and the straight path. When you examine it with the complex poynting vector you will find the twisted path has significantly higher losses.

    This all comes back to Maxwell's equations. Ohm's laws is a form of Maxwell's equations where some values are assumed and held constant, as are nearly all the formulas we use as electrical engineers. Thus we don't have to solve the field equations each time. But the field equations are still there, hidden by our simplified math.

    So knowing this we can take a short cut to find the extra losses in twisted field path. That short cut is to measure the additional resistance that the longer wire provides and find the I2R loss. Suppose we made the path straight and used the same length of wire? We can't but we could add a loop at the end. Then the losses in the loop would match the losses in the twisting (neglecting inductance/capacitance which changes slightly with geometry).
  7. Aug 9, 2015 #6


    Staff: Mentor

    What is the length scale involved? What makes you think that the layouts that you have shown are any different than a straight wire for the energy transfer? What sensitivity to the layout is predicted and not observed? What specific measurements were taken that differ from what should have been measured?

    You are simply assuming that the layout should change something without calculating anything and without even specifying what specific variable you think should change and how.

    Two very different field configurations may still have similar Poynting fluxes at the load.
    Last edited: Aug 9, 2015
  8. Aug 9, 2015 #7
    Yes, that's exactly what I'm doing, because I've been told for years that the layout can and does change things. As I said earlier (some clarifications in bold):

    "When I read practical engineering texts -- whether about filament windings or transmission cables -- I get the distinct impression that these fields around the wires are essentially unwanted side effects that we should strive to minimize by changing the layout (unless, of course, we're designing an antenna or a transformer or an inductive charger and thus want to maximize those side effects by changing the layout). On the other hand, the physicists appear to be telling me that these fields are not side-effects, but are the essential and primary means of energy transfer even in simple, hard-wired circuits."

    Two very different perspectives, I think. I'm trying to figure out the best way to describe electricity and electrical circuits (like tube guitar amps) to a ten-year-old. So I'm qualitatively (as oppsed to quantitatively) evaluating different conceptual models with that ten-year-old in mind.
  9. Aug 9, 2015 #8
    Yes, that thought did cross my mind. But there still appears to be a difference in perspective: are the fields the effect and the arrangement and movement of charges the cause? or it is the other way around? In another thread on this site from some time ago a poster was asking similar questions about electric and magnetic fields. I thought mentor jtbell gave a helpful response, the cricical statement in bold below:

    In what sense is energy "real?" In what sense are electric and magnetic fields "real?" ... You're venturing (probably without realizing it) into very deep philosophical matters here. Electric fields, magnetic fields, energy, and many other things, are all concepts that we use to explain the observed relationships involving physical objects and their motions. But "energy" is not a substance in and of itself; it exists only in the context of two or more objects. We cannot observe energy in isolation, or measure it directly. We can only infer the amount of energy involved in any process by measuring the positions and locations of objects before, during, and/or after that process, and performing some calculations. Similarly for electric and magnetic fields. After all, we define the presence of electric and magnetic fields by the observation that certain objects placed in proximity to each other move in ways that cannot be explained by simple contact-type pushes or pulls. I'm not trying to denigrate or belittle these concepts, or suggest that there's any useful replacement for them. They're amazingly useful, and I would not want to try to do physics without them. But we need to keep in mind the dangers of excessive reification of the concepts that we invent to explain what we actually observe. That is, we need to be careful not to associate "too much reality" to them.

    Makes me lean toward the former perspective (where the fields are effects and the arrangement and movement of charges are the causes).

    I like it. But it does make me think:

    1. The "shortcut" method seems to attribute the difference in performance to the greater resistance of a longer wire, not to a difference in the size and shape and interaction of the various fields. The latter, I presume, would be included in the "inductance/capacitance which changes slightly with geometry" that you mention at the end, and which you imply is negligible (relative to the greater resistance of the longer wire).

    2. The "shortcut" method, with its appeal to Ohm's Law (and thus E, I and R), implies that the important stuff -- the non-negligible stuff, the "action," so to speak -- is in the wires and not outside of them. Current is so-many electrons per second past a given point, and resistance is a physical property of the conductor. And it's easy to picture instantaneous energy transfer through a physical medium simply by referring the kid to a "Newton's Cradle" device without reference to "fields" of any kind.

    So again I find myself, at least for now, leaning away from the field model of energy transfer.
  10. Aug 9, 2015 #9


    Staff: Mentor

    What SPECIFIC things can and does the layout change?

    I am challenging you to be specific because you have not thought clearly through your own objection. The thing that you are asking about is a correct description of energy transfer (The Poynting vector) in EM. Your objection to the correct description is focused on the shape of the fields. You have made no connection between the shape of the fields and the energy transferred by the field. You assert that the shape of the conductor should have some effect on something, but you have not thought it through enough to say what effect it should have nor how that relates to energy transfer.

    By the way, whether wanted or unwanted, the fact that energy transfer between disconnected conductors can occur at all is clear disproof of the idea that the energy transfer occurs only within the conductor. That much should be qualitatively understandable by a 10 year old.

    Which dominates is a quantitative rather than a qualitative question, but that question must acknowledge the fact that qualitatively there is at least some energy transported outside the wire.
    Last edited: Aug 9, 2015
  11. Aug 9, 2015 #10


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    Welcome. We've had this discussion elsewhere about how to explain electrical energy in a physics compatible way to children. The 'shortcut' method is not an alternative to fields being the energy carrier. Ohms Law is just a simplification when the geometry of conductors including their physical lengths is small when compared to the electrical lengths so energy transfer is from reactive fields around those conductors not EM radiation into space between conductors. There are many ways to use analogy without forming misconceptions but I'm dubious that you will listen to the good advice here. Please prove me wrong.
    http://versys.uitm.edu.my/prisma/view/viewPdf.php?pid=17159 [Broken]

    To say "But there still appears to be a difference in perspective: are the fields the effect and the arrangement and movement of charges the cause? or it is the other way around?" is irrelevant as there is a synergistic effect in circuits where both are important to explain how the energy transfer system works as a whole in detail for source -> wiring -> load. The guiding and manipulation of electrical energy in fields is the reason we have circuits. A wire without EM energy is just a lump of metal, EM energy moving in space is just a wave. It's when we combine the two that cool things happen. To me that what you need to teach to young children. Focusing on one without the other is confusing when you look at it closely because it's a incomplete picture like explaining human reproduction with just the male or female half of the equation.
    Last edited by a moderator: May 7, 2017
  12. Aug 9, 2015 #11
    In AC circuits, the energy is in the fields. What the copper does is provide a place where currents can travel to make the fields.

    Since the copper isn't a perfect conductor it "slows" the fields causing losses. It does this by slightly changing the direction of the resulting field so it is not completely parallel to the wire (in the math this is a complex/imaginary shift).

    Some of the energy is directed to the wire rather than around the wire. That energy is lost as I2R heat. The amount lost depends on the amount of slowing which depends on how well the conductor can support the "eddy" current. (The words "eddy current" is usually used in magnetic type circuits and have some implications that this current doesn't, but the concept is similar.)
  13. Aug 10, 2015 #12
    Here are three that I've come across.

    Quoting from Merlin Blencowe's Designing Tube Preamps for Guitar and Bass: "Pairs of noisy AC wires (eg., mains and heater feeds) should be neatly twisted so the opposing magnetic fields around each wire are forced to occupy the same space, causing them to cancel each other out." So one thing that a particular layout can apparently accomplish is the neutralization of the magnetic fields around two wires.

    And here's a typical diagram explaining differences in transmission layouts:

    fields 3.jpg

    So it seems a particular layout can also "cancel field induction" and "balance capacitances to ground."

    Seems to me that magnetic fields that have cancelled each other out will transfer less energy than magnetic fields that have not cancelled each other out. I would expect "cancelled field induction" and "balanced capacitances" to also affect energy transfer in some degree.

    Everyone with a radio knows that energy can be transmitted over long distances by electromagnetic fields; I'm not arguing that point. I'm saying that it's hard for me to image that the energy transferred by the fields outside the wires in, say, a guitar amp, is significant when compared with the energy that is transferred by the electrons inside the wires (transformers, of course, excepted).

    Sure. The part that's a hard sell is the idea that the energy that powers our electric drill out by the tree-house is being transferred from the AC outlet, not through the 50-foot extension cord, but via invisible fields around the cord. Why? Because he knows everything around the cord is safe (it's those wires inside the cord we need to be careful with).

    And I don't think it will become easier to sell after the kid has been introduced to diagrams of fields in various configurations like this:

    fields 4.jpg
    Mainly because he's going to remember that drill by the treehouse and how it behaved exactly the same whether the extension cord was straight, messy, or wrapped up in a coil for storage.

    Agreed. But the author of the paper referenced in my initial post doesn't say that. His statement is unqualified, and his example is a battery, some wire, and a light bulb. Yet he claims:

    "It is this combination of electric field and magnetic field in the space outside the wires that carries the energy from [source] to [load]. Once the fields are set up, the energy travels through space, perpendicular to both the electric field and the magnetic field, at the speed of light."

    If he had said, "In this example, the electric field and magnetic field in the space outside the wires carries a relatively insignificant amount of energy from the source to the load -- the significant portion is transmitted through the wire itself," we wouldn't be having this conversation.
    Last edited: Aug 10, 2015
  14. Aug 10, 2015 #13
    I'm not sure what your point was is referencing that paper. All I got out of it was what I already knew: the way the subject is and has been taught to novices doesn't work anywhere near as well as it should. It may be true that some "experts such as electrical engineers and lecturers in engineering and physics... regard electricity as a field-like phenomenon, formed of endless loops." But those are clearly not the experts who have been writing the books for kids.

    I understand that. That's why I think the end-to-end guitar amp system is such a good circuit for beginner study. It's got both currents and fields all over the place: in the pickups, in the transformers, in the speakers, in the capacitors. But while it's true that the currents can affect the fields, and the fields can affect the currents, I think it's helpful to avoid philosophical chicken-and-egg questions with beginners by adopting one perspective or the other from the start. Right now I'm leaning toward the "certain arrangements and movements of matter create various electric and magnetic fields" perspective rather than the converse "certain electric and magnetic fields create various arrangements of matter" approach. We understand that the fields can affect the matter -- but only because the matter generated the fields in the first place. But I'm flexy, believe it or not. Show me a decent field-oriented electronics text for ten-year-olds and I'll see how it works when we try to describe a guitar amp with it.

    That's one way of looking at it. The problem is that two of the three important nouns in that sentence -- energy and fields -- are abstract and unfamiliar. And not just to kids.

    But we can't "combine the two" until we have the two in hand. And the usual starting point is matter, not field; we start with a wire and magnet (a hunk of matter with the atoms arranged in a particular way); or we start with a couple of chemicals; etc. I don't think anybody starts with an electric field; where, without matter, would they get one?

    We can tell the kid, in terms of your analogy, either (a) the male plants his seed in the female's garden; or (b) the female attracts seed for her garden via invisible and nearly irresistible forces. Both are true; but the former is more prosaic, more physical, and doesn't involve mystical forces and is thus an easier place to start. After all, every adult understands the mechanics of reproduction; but who can say he (or even she) fully understands the womanly wiles that surround it?

    Again, I'm not suggesting that we should focus on one to the exclusion of the other -- that's impossible in the context of a guitar pickup or a power transformer or a speaker. I'm saying (particularly in this thread) that I don't see how anybody can say that the primary means of electrical energy transport between a battery and a bulb is a field and not a wire.
    Last edited by a moderator: May 7, 2017
  15. Aug 10, 2015 #14
    Are you saying the energy is somewhere else in DC circuits?

    That's where you lose me. Where is the energy that makes the current that in turn makes the fields? It's obviously not in the fields, since they haven't been made yet.
  16. Aug 10, 2015 #15
    The other day I stumbled on the "Lamin's Loaf Lorries Model" (https://www.iop.org/publications/iop/2013/file_61204.pdf) developed by the students at the College of Richard Collyer and published by the Institute of Physics. Here's the gist:

    https://www.physicsforums.com/attachments/lorries-1-jpg.87013/ [Broken]
    The thing that struck me is that this model, unlike most other beginner models, makes a clear distinction between electrons and the energy that is being carried by those electrons. It is thus easy for the student to see, as he invariably and intuitively suspects, that while the current is the same on both sides of the shop (load), there really is more of something to the right of the shop than there is to the left. Not more electrons, but more energy being carried by those electrons (and dropped off, as heat or light, in the load).

    An added advantage is that volts -- and in particular, the unfamiliar units of measure associated with volts (joules per coulomb) -- can now be easily pictured: one volt is one loaf per lorry.

    What do you folks think of this model for a beginner?
    Last edited by a moderator: May 7, 2017
  17. Aug 10, 2015 #16


    Staff: Mentor

    Probably a book on guitars is not the best source for learning physics. This particular quote is simply wrong. You cannot neutralize the magnetic field by twisting two conductors around each other.

    What you can do is to concentrate the magnetic field. It becomes less intense away from the twisted pair, but more intense between the pair. This concentration of the magnetic field, in turn concentrates the Poynting vector, meaning that a bigger fraction of the energy transferred flows through the fields between the pair rather than the fields around the twisted pair.

    The conductor configuration with the most concentrated possible magnetic field is called a coaxial cable. It completely eliminates the magnetic field outside the conductors with no stray magnetic field at all. But there is still a very strong magnetic field between the two conductors. Thus there is still a place for energy to be conducted by the fields. Again, in even the most extreme conductor configuration, the magnetic field is concentrated, not canceled.

    The observed behavior of a twisted pair or a coaxial cable is entirely consistent with the proposed idea that the energy is transferred through the fields around the wire. If it were transferred only through the conductor then the conductor geometry would make no difference.

    That is a quantitative question, not a qualitative question. Are you interested in a quantitative answer? I don't have one for a twisted pair, but I do have one for a coaxial cable which is even more concentrated than a twisted pair.

    That is because it is not the EM energy flux that is dangerous, it is the current. The energy transferred by the field is given by the Poynting vector. But for safety what is important is the work done on matter. Energy that simply transfers in and out of the body without doing any work on the tissues causes no harm. You cannot feel energy flux, only energy deposition.

    The work done on matter is given (microscopically) by ##E\cdot J##, and because tissues are Ohmic the ##E## is proportional to ##J##. So the dangerous part of the electricity, the current, is indeed contained within the wires.

    Why do you assume it is an insignificant fraction when you have not done any quantitative analysis? You have no justification for thinking that your proposed statement is correct.

    You clearly understand that some fraction is outside the wire, but you have no reason to claim that it is insignificant. You are going from a qualitative statement "some energy is transmitted by the fields" to a quantitative statement "it is an insignificant amount". The latter is completely unjustified unless you have actually worked the problem.
  18. Aug 10, 2015 #17


    Staff: Mentor

    It is untenable.

    First, which side carries the loaves? Since the negative sign on the electron charge is just a convention, the loaves (if they are actual physical things) cannot depend on that convention. And since assigning one side to be 0 volts is also a convention it cannot depend on that either.

    Second, the velocity of the charge carriers is incredibly slow, on the order of mm/hr. So if you attach a 5 V source and fill up those charge conductors in the wire with 5 V loaves of energy then if you switch to a 10 V source it should take several hours before the new high-energy loaves reach the load.

    Third, for AC circuits the charge carriers never move more than a millimeter (usually far less), so you would never be able to transport loaves attached to electrons from the power plant to your house using AC.
  19. Aug 10, 2015 #18
    You seem to have a misunderstanding of energy. That's not surprising since few do (if anyone does). Energy is a form of stability (or perhaps anti-stability). It causes objects to assume more stable formations. Thus objects with a high field potential seek lower potential.

    Think of a steel ball on to of a cliff. The rock has energy because it is higher in the gravity field. Does that make the energy in the field? Or does the ball have the energy? That seems a philosophical question. To me the energy seems to be in the relationships.

    Now suppose we attach the ball with some others to a two string pendulum. You have likely seen such a toy. If you drop one ball, the energy transfers to another. Again. is the energy in the balls, or the field? To me it seems to take both.

    But unlike in gravity, in electricity there are two fields. One is electric and one magnetic. Energy can exist in the charges being higher in the electric field like the ball on a cliff. But it can also exist in a relationship between the electric and magnetic field without any steel balls (charges). We call these self supporting packets of energy photons. Since the energy can exist solely in the fields, but cannot exist solely in the charges, we tend to model the energy as being in the fields. (And remember electrons have little mass and move slowly, thus carry little energy under normal circumstances.)

    Please try to understand Maxwell's equations. Understanding how a time varying magnetic field causes an electric field and a time varying electric field causes a magnetic field is essential for understanding electricity on the level you are trying to grasp.

    The math for a DC circuit is different since the Poynting vector is designed for use with AC (RF) circuits. Still, there is an electric field fringing from the wire and a magnetic field around the wire. The energy transfer is the cross product of the fields. But with DC there is also an electric field along the wire. Its cross product leads into the wire and causes I2R heating.

    On a meta level, we are describing part of something called the "standard model" of physics. While the standard model has some holes in it, it is remarkably consistent with our observations of the universe. More importantly though this website is dedicated to teaching the standard model. While there are millions of other models, we only discuss the standard model here.
  20. Aug 10, 2015 #19


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    We say it because it explains what we measure when we build circuits. When we design circuits on paper with these rules, run the math and finally measure a real circuit built from those rules the measurements match the theory of energy flow in fields. In a vacuum tube what happens to the KE of the accelerated electrons inside the tube? Does it go to the speaker as electrical energy to create sound or is it disipated as heat on the tubes plate? The vast majority of anode heat comes from the kinetic energy of electrons as they strike the anode warming it instead of transporting electrical energy past that point in the circuit.
  21. Aug 10, 2015 #20
    Ah, but Merlin's book is no ordinary book on guitar amps. It's chock-full of all those formulas you guys like to talk about.

    Seems to me (and apparently to Merlin) that it depends on exactly how the conductors are twisted. If the conductors are twisted in such a way that the fields are "in phase" with each other then yes, we would expect concentration; on the other hand, if they're twisted in such a way that they are "out of phase" with each other, we'd expect cancellation. In fact, this transmission line illustration specifically speaks of cancelled, not concentrated, induction:

    fields 3.jpg

    I'm sure you can see the problem a beginner like me faces. Whom should I believe? Why?
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