[H8crilA]

No. DC energy also flows around the wire. And I mean around, entirely outside of the conductor, not in the skin or anything like that. In particular it's not the electrons that carry the energy, though they can receive it from the fields and depose inside the conductor (like in a light bulb).

Wires, or conductors in general, are so useful because they allow us to manipulate the EM fields and channel the energy very efficiently.

It's an very common misconception coming from circuit models.

(the movement of electrons, and thus the deposition of the energy via "resistance", may indeed be limited to just the surface of the conductor; this is what that calculator shows)

[jacquesm]

Complete nonsense, the current carrying capacity of a wire is directly proportional to the surface area of the cross section of the wire. If it were the skin it would be proportional to the circumference and it clearly is not. I have no idea where you came into this idea but it is just completely wrong. You can test it for yourself with $50 worth of gear.

[H8crilA]

You can invalidate the circuit theory with, well perhaps not $50 worth of hardware, but a bit more:

https://youtu.be/oI_X2cMHNe0

I'm not sure how do you plan to invalidate Maxwell's theory, which shows that energy flows entirely outside of wires, with $50. Or any other amount of equipment. It would be very much welcome in the physics community.

This misconception is even more widespread than "planes fly because of Bernoulli" because it's so incredibly useful when designing most circuits/PCBs. Though it is, fundamentally, a lie.

PS. Circuit theory is made to match reality for the case showed in the video via the concept of a transmission line.

[colanderman]

@H8crilA is talking about energy, you are describing current. Energy flow is the product of the electric and magnetic fields [1]; electric field within a conductor is zero, therefore energy flow within a conductor is zero.

[1] https://en.wikipedia.org/wiki/Poynting_vector

[H8crilA]

Yeah exactly. In particular a flow of current (movement of electrons or other charged particles, measured in Amperes) is not required for energy transfer, though it is a part of the efficient way of energy transfer via conductors/wires. Including in PCBs and even inside of integrated circuits.

[jacquesm]

> In particular a flow of current (movement of electrons or other charged particles, measured in Amperes) is not required for energy transfer

Of course it isn't, as any transformer or transmitter/radio would show you. But that's not what this is about. It's about as useful as telling architects to use quantum mechanics because that's the fundamentals of what they are doing or having every electronics design model each and every conductor as a transmission line. That's what Spice is for, to ensure that from an EM point of view the design is valid (and to ensure that you're not radiating EM).

But it's in the end a discussion about fundamentals and as you pointed out circuit theory is so damn useful that it gets you 'close enough for government work'. That there is a whole pile of field theory that you could use to model the same circuit is true but it isn't so damn useful and in practice would just complicate matters considerably requiring every electronics engineer to engage is high level math. Just like we're not going to ask carpenters and bricklayers (and architects) to take into account the fact that Newton 'got it wrong' and we should all be using Einstein's equations instead. But when you are designing satellites you should.

Engineering uses the tools appropriate for the task. If that tool is Maxwell's equations because we're dealing with stuff that should be modeled as a transmission line and the field component is the dominant one then so be it. But for most practical electronics circuitry you can use V/A/R just fine. When modeling capacitors and coils Maxwell's equations are applicable but you can likely still get away with approximations as long as you realize that that is what you are doing. When modeling a complex high frequency circuit things change rapidly and modeling your interconnects as transmission lines makes good sense because that is ultimately what they are and ignoring that aspect will make it much harder to design something that actually works.

So the statement that 'energy does not flow through a wire' makes sense in an EM theory view of electricity, which is fine for pedantry but won't get you places if you are moving bulk charge from point 'A' to point 'B' to get some useful work done. Just like EM theory in turn isn't correct either, the quantum physicist would tell you that your theory is 'just an approximation' and that you are 'doing it wrong'.

For the subject matter, antenna design the field is obviously the important part otherwise you're not getting anywhere at all. For DC to low KHz circuits that do not contain large inductors you will be able to keep things fairly simple. As soon as you start working with inductors you will have to 'level up' in your view of how the circuit works and if you don't you'll probably end up with something that is either sub-optimal or that subtly differs in its actual operation from what you think you've designed.

If you want to build GHz circuitry there is no way that you're going to avoid getting to know mr. Maxwell better, fact by then you'll be pretty intimately familiar with the underlying electromagnetic theory, it's unavoidable.

But for bulk energy transfer at very low frequencies it definitely isn't the skin that carries the energy, if it were you could replace all of your copper with foil and call it a day.

[colanderman]

> But for bulk energy transfer at very low frequencies it definitely isn't the skin that carries the energy, if it were you could replace all of your copper with foil and call it a day.

As I stated above, the copper emphatically does not carry energy. It can not, because the electric field in it is zero. What you are saying is true of electrons, it is true of current, but it is not true of energy. The energy is not contained "within" the electrons or is otherwise somehow tied to or carried by them.

The energy flows through the EM field as indicated by the Poynting vector which is only nonzero outside of copper. (Outside, as in -- through the void between power sources and sinks. Not the skin.) This field is induced by the flow of electrons.

Think of it this way: if energy were carried "in" the wires -- in this experiment, from the negative terminal of a battery to the light bulb (coinciding with the flow of electrons) -- what then is occurring within the wire connecting the light bulb to the positive terminal? Is energy flowing from the light bulb to the battery? If not, what makes this wire quantitatively different from the other such that energy isn't returning to the battery along this path? It's the same current after all (KCL), pointing back at the battery now.

It's not a matter of "circuit theory vs. Maxwell's equations" (and I don't know why @H8crilA is framing the argument like that). Circuit theory simply doesn't say anything about the flow of energy. It deals with current flow and voltage potentials, but not energy flow (except in the cases of transmission lines and transformers). It's not "wrong" or an "approximation" in this sense -- but there's nowhere in a circuit diagram you can point to and say "this is the path the energy is following". (Unless you start decorating the diagram with arrows between power sources and sinks, which then starts to look a heck of a lot like the Poynting vector.) But if you say instead, "the energy flows through this wire" (which again, circuit theory does not claim), this is mathematically inconsistent in even the simplest circuit, since, after all -- energy does not flow in circles!

I suppose one could augment circuit theory with a notion of "energy flow through a wire" by equating that to product of the current through the wire and the potential between that wire and some fixed reference (e.g. ground). This would be mathematically consistent but not give meaningful physical results -- the battery-light bulb circuit above, if tied to an arbitrary potential high above the reference, would indicate a proportionally arbitrary massive amount of power flowing "out" of the battery, and slightly less than that amount flowing back "in" to the battery. Maybe some EEs conceptualize circuits this way (maybe even I do unconsciously?) but I'm not aware of this being standard pedagogy.

[jacquesm]

You have cause and effect switched. The field is the result of the flow of electrons, not the other way around. That makes for a nice shortcut ('it's all fields') but without that flow of electrons through a conductor carrying current there is no field. Fields are a direct result of moving charge and electrons carry charge. This is symmetrical, fields in turn have the potential to move charge. The fact that some fraction of those fields extends outside of the conductors (they have to, they are at right angles to flow of the electrons in the conductor) is not a very good reason to suddenly leap to the conclusion that all 'energy is transferred outside of the copper' until you actually use that component: such as in a transformer, or to model parasitic inductances between conductors. And then you'll find that for most wire thicknesses and most frequencies (except for special HF 'litze' wire) the bulk of the energy is still transferred within the circumference of the wire. That's because the EM field of a single electron is tiny and extends in theory out into infinity but in practice and at normal currents and frequencies is actually very limited.

The reason why people under normal circumstances would not decorate the diagram with arrows between power sources and sinks is simple: it would be redundant. Just like we don't draw capacitors, coils and resistors over every wire. We all know they are there but for most practical work you can ignore them, in fact you do your level best to ensure that those parasitic components are as small as you can make them to ensure your circuit works as intended. But once they become more dominant (which already happens at very low frequencies above DC) you have to start taking them into account, but for most regular applications you will still find that the larger part of the field is constrained within the wire and only a tiny amount extends outside of it.

So, in an extremely pedantic sense you are right: for an infinitely thin wire the EM field will lie completely outside of the wire. But for real world wires the bulk of the field is constrained within the wire.