Dave, you should correct your video, the errors are too big.
At minute
3 something ops 9:30 you say that at DC the Poynting vector would be pointing towards the battery. This is
wrong.
At minute 41 something you show a picture of a resistive wire from Feynman that shows the Poynting vector going inward, into the wire. Well, that's a resistor, power is getting in to be dissipated.
Even at DC the Poynting vector is going out from the battery, then goes nearly parallel to the copper wires, and then finally points inside the resistor. You misread Feynman (who, by the way, for fig 27-5 explicitly talks about 'resistive wire' which has a resistance and a voltage drop).
Simple experiment:
9V battery shorted by copper wire: the wire gets hot. Poynting vector pointing out of the battery and into the wire. (the wire is the dissipative element in this context).
9V battery with a 100 ohm resistor connected via copper wires: the resistor gets hot, the wire doesn't. Poynting vector directed out of the battery, nearly parallel to the wires, and then plunging into the resistor. As correctly shown by Veritasium (for DC)
And no, skin effect has nothing to do with that.
EEVblog 1439 - Analysing Veritasium's Electricity Video
Dave analyses Veritasium's video "The Big Misconception About Electricity" and how energy flows in the Poynting vector in the electromagnetic field OUTSIDE the wire instead of inside the wire.
00:00 - Veritasium's video "The Big Misconception About Electricity"
00:32 - Rection to the points in the video
01:11 - This is a bit MISLEADING!
02:28 - Electron drift
03:51 - Engineers use different tools and theorems
04:27 - Every electrical engineer knows this
05:17 - Everything he says is correct
08:24 - What is current?
09:30 - He doesn't address this in the video. Poynting vectors at DC
11:12 - How the lightbulb works
12:41 - At the physics level, it's correct
14:11 - My only problem with this is...
15:08 - Is it just an academic discussion?
16:17 - The undersea cable is just early transmission line theory
17:20 - So what is the answer to the question?
22:06 - What about skin effect and DC?
25:44 - Let's simulate this and answer the question
29:18 - Transient analysis
33:00 - DC Steady State analysis
34:28 - The quantitative values don't matter
38:25 - But what about DC steady state?
40:24 - What does Richard Feynman think?