The electric field is very tightly constrained around the wire. The amount of energy that reaches the light through the gap is incredibly small, not nearly enough to turn on a real light bulb. The bulk of the energy does indeed have to take the path through the wire. I find that video usually leads people to an even less correct understanding than the marbles-in-a-tube analogy.
The Veritasum video can essentially be summarized, "fun fact: two parallel wires act like an antenna, and an extremely small amount of energy reaches the other end before the rest of the energy takes the long path through the wire.
I'm not sure circuit theory states that energy flows within wires? Current, yes, but energy transfer is the product of current and voltage, and voltage of course exists only between wires.
The Poynting vector is the obvious choice but we cannot do the experiment to tell between the various possibilities one can get by adding more terms that obey the constraints.
Energy does flow 'inside' a wire at low frequencies. The skin effect gets higher and higher as the frequency goes up until you reach a point where it is all skin effect. But even that 'skin' isn't idealized it definitely has a thickness, about 30 u at 5 MHz and 6.5 at 100 Mhz.
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)
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.
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.
@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.
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.
> 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.
Someone actually went out and tested this: https://www.youtube.com/watch?v=2Vrhk5OjBP8
The electric field is very tightly constrained around the wire. The amount of energy that reaches the light through the gap is incredibly small, not nearly enough to turn on a real light bulb. The bulk of the energy does indeed have to take the path through the wire. I find that video usually leads people to an even less correct understanding than the marbles-in-a-tube analogy.
The Veritasum video can essentially be summarized, "fun fact: two parallel wires act like an antenna, and an extremely small amount of energy reaches the other end before the rest of the energy takes the long path through the wire.