So if energy flows not in wires but near the surface, then if we take a fairly large sheet of copper, ground it, drill a hole in the center with the hole diameter being very close to the wire diameter, and run the wire thru the hole, then we will block the flow of energy (assuming the hole walls are so close to the wire surface but not touching it ) along the wire surface , and therefore when we close the switch the load will not get any energy in DC steady state because no electromagnetic field can break through the shield . I do not think anyone here would believe that at DC no energy will flow into the load in this experiment. Therefore the claim that energy flows not in wires is bogus.
@Bud: The magnetic field at DC will go straight through a copper plate. The electric field AKA voltage difference will crowd into the gap. From this time of night I can't see how that makes you wrong. The bulk of the magnetic field will be in a place with no electric field.
We're both wrong. (Sort of.)
I just did the integration (in Excel) of this situation:
https://database-physics-solutions.com/buy.php?superlink=use_the_poynting_vector_to_determine_the_3948(..after being unsatisfied with the Wikipedia one at
https://en.wikipedia.org/wiki/Poynting_vector - what is W? This is my main problem with mathematics - people assume you "know" or are willing to go searching from zero context, forward through that material or something else unspecified)
It describes a coax carrying DC. Supplies formulas for electric field and magnetic field using radius r, multiplies together for each r to give the Poynting magnitude at that r, integrates for r over the insulator space, then invokes some magicks to prove something that I am not interested in. I summed Poynting magnitudes in Excel with a radius step of 0.1mm (also tried 0.02mm just to be sure).
Case 1 is coax with 2mm centre conductor (a=1) and 10mm ID shield (b=5).
Case 2 is that same cable, but with a slug of copper (or whatever) inserted into the space, such that it leaves a 1mm gap to centre conductor, and is almost touching the shield but connects at one point (say via a very thin ring round the middle, a tack weld, or tiny piece of wire). The idea is so no current passes along the slug therefore leaves the magnetic field alone, but is electrically connected to the shield so electric field compacts into the smaller gap to the centre conductor. The purpose of this is to test "The bulk of the magnetic field will be in a place with no electric field.", by that I mean a space that once contributed to Poynting power is simply deleted without change to one of the multiplicands (the magnetic field). You'd think this might result in a different number for the sum of the products.
I put 12V on it, and 1A through it. Result for case 1 popped out with the expected 12W (actually -12.3042 because I got a and b round backwards, the excess because the sum over r = 1 to 4.9 step 0.1 is skewed to smaller diameters, out of interest if I change the start number to 1.05 so the table runs to 4.95, the result is -11.997). Verifying that my numerical integration technique works.
Result for case 2 is -12.44361527 (-11.9946 with centred steps, not trying to be confusing, it's just the process and demonstrates the "imprecision" I raised earlier) - confirming that the squeeze in electric field is enough to 'exactly' offset the deletion of the area which no longer contributes to Poynting power.
This confirms what bdunham7 was saying about the results being exactly the same however a circuit is twisted or encased. I don't think anyone was expecting Poynting's math not to work, so hardly a surprise it does, and from looking at the equations it's obvious why there is a problem with Bud's and my intuitions: H = I/2/pi/r irrespective of the size of the cable (I've 'proven' a hidden V=IR in something before, even resorting to graphing it, so this isn't quite as silly as it sounds!). The magnetic field used to calculate the Poynting result in a sense doesn't depend on anything other than the current - a proxy for it? Shifting the 'current' to a place where it can be in line with the electric field calculated in its space between the pressure difference, completely orthogonal to everything else. What more unrealisitc way of measuring power could there be? After all there remain physical charges actually moving in a current of fluid within the copper wires, exerting an actual mechanical pressure (including pressure drop in the load).
On the other hand it works for (and is completely consistent with) AC, with its ability for current to seemingly jump out of the wires and into empty space, into a physical manifestation of that magnetic field. And I've got no complaint over another transverse field (electric) being the driver of energy transfer in circuits, whether that be AC, DC, electric, fluid, string, chain, rotating shaft or whatever.
How to test for its position? A thought experiment with a lop-sided conductor pair, perhaps with breaks in the current path as above. Or use microwaves, something similar with fets switching the current paths and a great big roots-blower-ish beamline centrifuge to weigh the data.
Time to call it a day (as in, it's getting late again). I think I'll pick a side, and choose the mechanical explanation, that is power flows in a combination of wires and the voltage difference. Otherwise it becomes a bit of a circular definition, where everything is "energy" but which behaves like particles.
(I can attach the spreadsheet if anyone wants - it ain't pretty.)