After watching Veritasium second video on electricity (references at the end), I have some doubts about where the majority of the energy flow actually happens. The reference experiment is the simple circuit made of a battery, switch and load (resistor).
Feynman Lectures: In Volume II, 27-4, Feynman remarks that:
we must say that we do not know for certain what is the actual location in space of the electromagnetic field energy
which puts into question if the common interpretation that the Poynting vector defines the direction of energy flux (power flow) is indeed correct. It is well-known that Poynting's Theorem is valid only on a closed surface, but Feynman remarks seem to point out that, even in that case, the energy of the EM field cannot be localized. Was Feynman too cautious in his statements?
Initial EM field: Looking at Veritasium thought (and also real, albeit scaled-down) experiment, after the switch is closed, an EM field radiates outward (at the speed of light) from the switch towards the load. This field, while generating a current which is orders of magnitude above leakage current, still generates only a transient (weak) current, which is greatly surpassed by the current in the stationary regime. Thus, it seems safe to say that this transient does not carry the majority of the energy.
Energy flux: Considering real-world conductors (perhaps excluding super-conductors), my question boils down to the following: is the majority of the energy carried by the outward EM field located at the surface (or, to be more precise, extremely near the surface, but still outside) of the conductor? Or is it, instead, being carried by the EM field inside the conductor?
Skin Depth: Since our experiment is in DC steady-state, skin depth should be negligible, but I would be really surprised if it turns out not to be so.
Simple "everyday intuition" seems to suggest that the majority of the energy flow should be inside the conductor (with bigger conductors able to carry more energy), but that is generally not a reliable indicator of scientific accuracy.
P.S. I do not know if the answer to this question is greatly affected by framing it as a classical electrodynamics problem, or as a quantum electrodynamics (QED) problem. Although I studied the basics of quantum mechanics, I didn't study QED, so I would really appreciate if someone with that kind of background can shed light also on this.
Other questions on Veritasium videos, with explanation as to why they are different:
- Speed of Light - independent issue, already clarified that there is no violation of causality;
- 1m/c seconds - irrelevant in my question, which is not about time, but about energy;
- Alternate explanation for energy flow - related, but doesn't answer my question, which is where the majority of the energy is located (spatial distribution of EM energy), not if (or why) there is EM energy near a wire;
- Insulator, Switch location, larger gap - variants of Veritasium experiment are proposed and questions about time are asked, again, no energy flux is discussed;
- Loop of wire - variant of Veritasium experiment, again about time and not about energy;
- Veritasium vs. Science Asylum - related, but focuses on what happens during the transient, and (again) does not clarify the spatial distribution of EM energy near a wire;
- Question on electrical currents - again about time;
- EM field around a conductor with current - question about why we don't get electrocuted by the EM field around a wire;
- Simple circuit - again about time.