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The introduction chapter of "Sound System Engineering, 4th ed." has a section titled "Fields", and in it some quotes that state energy is not transmitted through the wire, rather outside of it. I was taught that electric current travels through the wire and that it's a very factual thing! But...

In this link you can read the section and the quotes. Like these:

Oliver Heaviside, 1882, from his book, “Electrical Papers,” Vol. 1.“Had we not better give up the idea that energy is transmitted through the wire altogether? That is the plain course. The energy from the battery neither goes through the wire one way nor the other. Nor is it standing still, the transmission takes place entirely through the dielectric. What, then, is the wire? It is the sink into which the energy is poured from the dielectric and there wasted, passing from the electrical system altogether.”

John Ambrose Fleming in 1898 wrote, “It is important that the student should bear in mind that, although we are accustomed to speak of current as flowing in the wire in one direction or the other, this is a mere form of words. What we call the current in the wire is, to a large extent, a process going on in the space or material outside the wire….”

And also

Those of you who feel that many of the ideas are not mainstream should find a copy of “Standard Handbook for Electrical Engineers” by Donald G. Fink and H. Wayne Beaty.…there is a section entitled, “Electromagnetic Wave Propagation Phenomena.”

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.”

There's an interesting analogy in the book: imagine a building with walls and corridors. People travel in the corridors. The circuit lines (wires) are the walls, and the spaces are the corridores. Energy travels in the corridors.

This has been melting my brain. I've searched about the subject, but nothing made it click. I know Lenz's law, and in my mind the conceptual view was: "potential difference from a battery applied in a circuit will make current flow through the wire, and this current will create a magnetic field around it according to Lenz".

The question is: if electric current is an abstraction, if energy from a battery does not go from one point to another, what is going on? What's the conceptual view that I should learn and use?

I also found these:

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  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. $\endgroup$
    – Buzz
    Commented Jun 19 at 23:11
  • $\begingroup$ Heviside's book is from 1092, not 1882. $\endgroup$
    – my2cts
    Commented Jul 30 at 21:28

2 Answers 2

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When a current runs through a metal wire the electrons are constantly accelerated by the electric field, converting potential energy into kinetic energy. By scattering this forward momentum is randomized and hence the excess kinetic energy is converted into Ohmic heat. Now the standard theory tells us that this energy is not coming through the wire and carried by the electrons, no, it is brought in from outside the wire as described by the Poynting vector.

This does not make sense. There is a problem with the description of the energy-momentum, although its divergency is obviously correct.

There is also a problem with electromagnetic spin.

For a discussion of these points and a solution I refer to my paper A theory of electromagnetism with uniquely defined potential and covariant conserved spin, Eur. Phys. J. D, vol. 8, p 9-12 (2000).

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  • $\begingroup$ Transfer of energy to a moving charged particle in vacuum does not require other charged particles behind it carrying that energy and transferring it by some kind of mechanical contact, or "push"; external electric field of distant sources is enough. So when such particle accelerates, EM energy is brought into the particle from outside the particle. There is no problem with this, it has to be that way, if the particle is to change its energy. $\endgroup$ Commented Jun 19 at 23:09
  • $\begingroup$ So why would there be a problem with analogous situation in the wire? There are many more charged particles there, but these do not transfer substantial energy to each other. Instead, they get their energy, which eventually turns to heat, from the work of external electric field. So the energy may, again, come from the outside of the current-carrying region of space. It makes sense and there is no real problem with this, other than it does not conform to the preconception that energy has to flow inside the wire. Electric wire isn't a pipe with running water. $\endgroup$ Commented Jun 19 at 23:11
  • $\begingroup$ In such a pipe, each element of water is pushed against resistance only by gradient of pressure, due to contact forces due to other elements of water in front of and behind it, so energy flows only where the water is - inside the pipe. But in a wire, an element of free charge is "pushed" against ohmic resistance not merely by contact forces from the other free charge elements nearby (there is no "pressure gradient" in the free charge "gas"), but by external electric force due to distant surface charges and charges outside the wire (e.g. battery). $\endgroup$ Commented Jun 19 at 23:46
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    $\begingroup$ Thanks for the answer! I strongly disagree with the downvotes - not because I know the right answer, but because this was a question about something completely counter-intuitive and that goes against what's currently taught. $\endgroup$ Commented Jun 20 at 16:51
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    $\begingroup$ @EnzoFerber My 2000 paper was completely ignored. I went into industry a had a great time. Now that I’m retired I’m picking up the fight again. Your question is excellent. Don’t give up your physical intuition. $\endgroup$
    – my2cts
    Commented Jun 20 at 17:34
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There are many versions of how electric current flows in a conductor . We provide another version that you can actually check. It is well known that all real objects have their aura, which is virtual electrons that are repelled by real electrons of objects. An electrical wire also has a coat of virtual electrons, and the existence of these virtual electrons can be verified using the VEGA-12 device or the biolocation method. But when the wire is part of any electric circuit and this circuit is under voltage, then the virtual electrons disappear from the surroundings of the metal wire, which is indicated by the results of the test by the methods mentioned above. Most likely, virtual electrons became real when voltage was applied to the electric circuit. They created a real current. Real electrons in this case have their spins equally directed, which creates a magnetic field around the current-carrying conductor. After disconnecting the wires of the electric circuit from the power source, a coat of virtual electrons appears around them again. Similar phenomena also occur in electronic lamps and electron-beam tubes, etc. Similar processes take place in autoelectron emission .

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