Yes, this is the correct answer.
When you try to explain the concept of “energy flow” in electric circuits, P = IV isn’t very useful. You have to whip out Maxwell’s Equations.
Yes indeed. And once you’re familiar with the protocols of the Poynting vector it all becomes really clear. Inside the conductor the E field is longitudinal and the PV is therefore radially inward, thus supplying the power necessary for ohmic heating. I remember how I neat I thought that was when I first worked it out. (This also shows very clearly that the energy does not propagate inside the wire.)
How much of an EM wave is there in connection with a constant voltage difference between two points, such as betweem the terminals of a voltaic cell?
Not in a public place, you don’t! I don’t care what you call “it”. This is a family-friendly forum! 
I’ve nothing to add to the already excellent explainations except to reinforce the notion that electrical conduction is not physically analogous to water flow through a pipe, even if that is a convenient metaphor for explaining the relationship between voltage and current. As noted, the electrons live in the metallic lattice, shared between the atoms via metallic bonds which are sort of like covalent bonds, but looser in relationship. The current isn’t made of electrons moving though the wire (though with a direct current that does occur to to a limited extent) but rather, like waves in the ocean, by the electrons jumping “up and down” in sequence. It isn’t electrons, but energy, that is transferred.
Stranger
Quoth Fridgemagnet:
You do? Why would you need a silly thing like that?
We’re chasing our tails here guys. The movement of charges is what creates potential differences. In a voltaic cell, chemical effects result in positive charges migrating to one terminal and negative charges to the other. When rain drops have been jostled around for awhile they pick up charges, usually electrons, and then when they fall from the clouds they take the charges with them resulting in a potential difference between cloud and ground. In an generator the conductory moving through a magnetic field moves electrons to one pole which becomes negative with respect to the other pole which now has a deficit of electrons.
Moving charges create potential differences and potential differences move free (lightly restrained or unrestrained) charges.
The charges in all circuits don’t really move very fast so they don’t move very far in short times. Just the same, if one DC ampere flows for one second a total of about 6.24*10[sup]18[/sup] electrons have moved past a given point. If that point is the negative pole of a battery then that many electrons have left the battery. And the same number have returned into the other terminal, but again not the same electrons.
In one half cycle of a 60 Hz AC current of 1 Amp. rms 4.68*10[sup]16[/sup] have left the negative pole of the generatory and the same number, although we can’t say the same electrons, returns into the generator.
It’s late at night here after a busy weekend, so I may be beyond all reason, but this looks just… wrong to me. A vacuum tube seems like one of the situations where electrons really do flow – in this case from cathode to anode. You can even measure their velocities spectroscopically. You can bend their trajectories, throw a few extra electrodes and a phosphor into the mix, and see the results visually (e.g in an oscilloscope). Could you explain your claim, or am I just somehow being whooshed by a subtle point that you’re making?
I agree.
You can measure a potential difference without referencing a common/ground.
I have a Fluke 87 handheld multimeter. It is battery operated, and has a thick rubber case. Electrically speaking, it is isolated from the earth. Yet I can measure the potential difference between two points.
Are you saying it’s impossible for a potential to exist unless there are moving charges?
Let’s say there’s an electron and proton floating around in space, and that the distance between the electron and proton is always 10 inches. A potential will exist between the electron and proton, yet there are no moving charges.
A battery is a charge pump. When you connect a load to a battery, it will pump charges “uphill.” But a potential will exist across the leads of a battery even when there’s no load (i.e. when charged particles are not being pumped uphill).
My grandmother (family legend tells) used to worry about changing a lightbulb, in case all the electricity leaked out the exposed socket and formed a pool on the floor. It was therefore doubly useful to stand on a chair while you did it.
True, but it won’t help you measure the potential difference between 2 clouds. Luckily we don’t normally have to do this, and with the trivial case the reference is whatever we define it to be.
And I shit you not about the lack of actual electron flow through a capacitor (leakage current due to imperfect dielectrics notwithstanding), though I may cheekily reserve the right to change my mind about my previous assertion about the same effect in tubes. I may have been misled by the otherwise reliable Mr Tone Lizard - this page does however contain a neat illustration of how capacitors work at an electron level. Scroll down past all the loadline graphs to find it.
As for tubes/valves, the consensus opinion seems to be that there is actual electron flow from cathode to anode (not just apparent electron flow, like in a capacitor), and these electrons are provided by a hot cathode wire. I stand corrected, and will slope off quietly now to the Humble Corner.
I still don’t understand your point here.
First of all, you can measure the potential difference between two clouds using a voltmeter with very high input impedance (e.g. an electrometer). Secondly, we really don’t need to define a “reference,” though in most situations it certainly makes the system easier to understand when we do.
I don’t really have a major point to press home, so worry not. The cloud thing was only an example of having a handy universal reference (the Earth’s earth), and though it’s not easy measuring earth-cloud potential, it’s far more difficult to measure cloud-cloud potential due to the impracticalities of having to place your measurment terminals several miles apart, both in the middle of clouds. Much easier to send up little rockets or balloons on earthed tethers. Assuming they don’t induce a lightning bolt, which they would if the cloud was brewing one. Anyway, it’s a digression.
I have an apology to make to Mr Tone Lizard, who I accused of misinforming me earlier about electron flow in valves/tubes. Upon further reflection it seems I have misinterpreted his statement that there is no actual electron signal flow across a capacitor or valve/tube, and indeed this is the case. For the valve/tube, the signal voltage across the grid (relative to the cathode voltage) directly affects the signal current flowing from anode to cathode, and though there are indeed real live electrons streaming from the cathode to anode, no electrons pass from the grid to anywhere else, so in effect you could say the actual signal path for electrons is stopped dead at the grid terminal.
No, I’m saying that the potential of a point in the vicinity of a charge is the work done (either on the charge or by it) in moving a unit charge from a point far, far away, to that point.
Actually I need a mea culpa here because the post of mine in question here wasn’t precise enough to convey the point I was trying to make. Which, of course, might not have been worth making in the first place. 
The statement was made that charges don’t have to move in order to transfer energy. My point is that whether or not they have to move, they do.
It is easy to write “Let’s say there’s an electron and proton floating around in space …” You wrote it and I just copied it. And that’s all very well for a textbook, ideal case example. However, in actual fact the two charges had to get separated somehow in the first place because they would rapidly come together and stay there othewise. My original statement would have been better put as; for a potential to exist charges have to have moved at some time in the past or be moving apart now.
In every case in the macro world where we live charges have to either have moved apart in the past or be moving apart now for a potential to exist.
And for energy to transfer the charges that were separated by doing work in them first place have to come together again in order to get that work back. Not the identical charges of course, but charges of equal magnitude. And in reuniting they pass through some kind of a device that converts the mechanical work in separating them into other mechanical work or some other form of energy.
Good question David. DC circuits definitely cloud the issue, but not nearly as much as a setup with a stationary magnet and a stationary charge.
In any case if you’re talking about an open circuit then there’s obviously no power propagating, no B field and no Poynting vector.
However if there’s a load connected then you have an initial transient wave that sets everything up, followed by a steady state E field between the conductors and a circulating B field around the conductors.
Outside the conductor the PV still points to the load, at the surface it still points radially inward, and the energy flux density resides in the Poynting field. So there’s steady state fields but no wave as I’m sure you knew.
There isn’t any doubt that the fields are what cause the charges to move. However I think it is more direct to think of the charges as carrying the energy, chemical, mechanical, or thermal, that was put into the source and delivering it to the load. Especially in the case of DC. It’s a little murkier, OK it’s a lot murkier, with AC but I still prefer it.
In electrodynamics there is no way to determine exactly where the energy is:
But in the case of an EM wave it’s pretty clear that the energy resides in the wave and not in the conductor since there is no conductor. So why not carry this given over to circuits, especially since the EM wave inside the conductor travels so much slower than the energy actually propagates. Granted that with DC there is no wave but there is a Poynting field.
Anything wrong with the old standby of 1/2(E[sup]2[/sup]+B[sup]2[/sup])? So far as I know, that works in every context in E&M, and also in GR, where the localization of energy actually means something.