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"Veritasium" (YT) - "The Big Misconception About Electricity" ?

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rfeecs:

--- Quote from: SandyCox on January 05, 2022, 07:13:35 pm ---
I did take the direction of the vectors into account. So did Haus and Melcher when they calculated the integral of the Poynting vector over the outer surface of the rod and got the same answer as I did.

What you are doing is exactly the misinterpretation of the Poynting vector I am referring to.

You have to calculate the integral of the Poynting vector over the total outer surface of the rod. You then have to add up the contributions from the different surfaces before coming to a conclusion. You cannot conclude that Power is entering the rod through a particular surface by looking at the integral of the Poynting vector over that surface.

--- End quote ---

OK, then I don't understand your point.  I thought you were saying there was some problem with the math of the Poynting theory.  Now you seem to be saying that the Poynting theorem gives the same result as P=IV.  That is no surprise and there is nothing inconsistent.


--- Quote ---I suggest that you do the following:
Calculate the integral of sigma times E dot E o
ver the volume of the rod and the washer. This is the amount of electromagnetic power that is converted to heat (dissipated) in each of them. Now look at the problem from the circuit analyses point of view and calculate the current that is entering the rod and the washer. You will see that all the power that is transferred from the voltage source to the rod is dissipated in the rod. Likewise, all the power that is transferred from the voltage source to the washer is dissipated in the washer, i.e. there is no net transfer of power between the washer and the rod.

--- End quote ---

Again, you are saying P=IV.  So what?

Apparently you are concerned that the picture of the Poynting vector pointing from the disk to the rod doesn't seem to make sense.  This is similar to the circuit with three resistors discussed previously.  It looks like power is flowing from one resistor to the other.

So an explanation would be that power flows out of the power supply, to the space on the left of the disk, then all the power flows into the disk, some of that power is dissipated, the rest flows to the rod through the space between the disk and the rod, and that power is dissipated in the rod.

It's not a pretty picture?  But it can still account for what is happening and satisfy energy conservation.  As you say, just integrate over the closed surfaces and both conservation theorems still work at DC.

Sredni:

--- Quote from: SandyCox on January 03, 2022, 12:30:23 pm ---
--- Quote from: Sredni on January 03, 2022, 11:01:33 am ---
--- Quote from: SandyCox on January 03, 2022, 10:54:41 am ---Ascribing meaning to the Poynting vector at a point leads us to the wrong conclusion, as shown by Fig. 11.3.1.

--- End quote ---

I didn't see Haus and Melcher recant what they wrote

"Even with the fields perfectly stationary in time, the power is seen to flow through the open space to be absorbed in the volume where the dissipation takes place."

Did you?


--- Quote ---I’m not quite sure what you a trying to say by “glowing red hot”. Are you saying that energy is now transferred through thermal radiation?

--- End quote ---

No, I'm saying that by making rod and washer of very different materials you can have one glow red hot while the other stays cool, and viceversa. There still will be Poynting field lines in the space inside the can and they will account for the difference between the total power delivered by the battery and the power absorbed by the rod.
In one case you will see a lot of lines coming out of a cool washer to impinge into a red hot rod.

--- End quote ---

On the next page they say:
" we illustrate the danger of ascribing meaning to S evaluated at a point, rather than integrated over a closed surface."

I'm not sure why you are dragging thermal issues into the argument. We can also make your resistors glow, but why would we? Add a cooling system if you are worried about conductors glowing red.

The point is that there is no power being transferred from the washer to the rod. All the power is accounted for. Misinterpreting the meaning of the Poynting vector leads us to incorrectly believe that power is flowing from the washer to the rod. Please do the calculations. You have all the information you require.

--- End quote ---

I used the cool washer and hot rod as an as an example of how counterintuitive it would seem to see power flow from a cool object to a hot one. And to highlight that the energy would not come from the cool washer, but from the battery.
Anyway, what follows was written a day or two ago. I had to draw and scan a few pictures and that took time, so some points might already have been discussed.

1) It is undeniable that there are both an electric field and a magnetic field in the space between (and more generally around) the wires. One can measure them.
But most importantly, one can use those fields to do work. Can we say that we are extracting energy from the fields?
I can use the E field to make an electric dipole rotate, for example. Or to slow down dust particles in the space near the wires and make them pile up. I can also use the B field to make a magnetic dipole rotate, like a compass needle in the space near the wires.
It takes energy to make that mechanical energy appear.


2) Where does that energy come from? It is said it comes from the fields.
Granted, the fields in the static case are not linked to one another as the E and B field of an EM wave (more on this in point 5 ), but they are still both generated by charges in your circuit.

     static charges:   surface charge on the conductors' surfaces and at the interfaces between materials
     moving charges: currents flowing in the conductors and displacement currents in dielectrics

the charges moving inside the conductor are the result of the field generated by the static charge on the surface, which in turn is distributed in that way because the battery has been connected to it.

Consider a charge magically materialized in the space between the wires of our circuit. The moment the electric field puts a charge in motion, a magnetic field appears, and the Poynting vector shows the charge 'stealing' energy from the field (changing it).If I put mechanical energy in to force a charge against 'its will' (for example to put it there from the 'chargeOort cloud' at infinity), I will end up adding energy to the field. Again, a Poynting vector field will appear to show energy getting into the field. If I move the charge back and forth slowly (quasistatically), I keep adding and subtracting energy to the field with no radiation.


3) Let's get to the Poynting vector at DC for the resistor alone. Oh, by the way, I hope it is clear that both rod and washers in that Haus & Melcher example are the resistors - the conductor is the cylindrical can.

For a homogeneously cylindrical resistor where a constant DC current is flowing the Poynting vector is directed radially in and decreases in magnitude to zero when it reaches the axis (because that's what the magnetic field magnitude inside does). Is energy disappearing from the universe? Of course not, it just gets converted into something else. The following figure shows the Poynting vector field for a resistor with a 5V potential difference across it:


fig Poynting for a cylindrical resistor - three cases

All textbooks dealing with energy balance by means of the Poynting field say we must always integrate over a closed surface, so all we can say is that, thanks to the distribution of surface charge on the circuit elements and the ensuing currents flowing, energy is getting into the resistor from outside.

You point out an alternative way to compute the power absorbed by the resistor that does not need to consider the electric and magnetic fields in the space around the conductor and circuital elements. Fine, instead of considering the whole of B you just take j into account. By resorting to the non uniquely defined potential function phi (with that arbitrary additive constant...) this method leads to an infinity of different configurations of energy flows. Same resistor with 5V potential difference, but different choice of the zero potential reference.



fig alternative Poynting for a cylindrical resistor - three cases

Luckily we must only consider the results of integration over a closed surface, still, the phi J representation appears to be weaker than the ExH representation.
Adding to the 'potential' nonuniqueness problem (which, one might argue, affects the ExH representation as well since we can still add an arbitrary zero-divergence vector to ExH), this alternative method is not a general method that takes into consideration the whole physical system. In fact, it does not take into account what happens in the space around the conductors and elements. It ignores the surface charges that give rise to the field inside the conductor, and only considers what happens where the current is flowing. In fact, it's blind in the space between conductors.


4)  You say that in Haus and Melcher's example, all energy is accounted for and therefore there is no need to have any transfer between washer and rod. But this is also true in the orange parallel resistors circuit: there is no energy transfer between the first resistor and the second one. In fact the first resistor takes in a net power equal to the power it dissipated in heat via Joule heating. (side note: The first resistor just happens to be in the way of the power transfer from battery to the rest of the circuit. It is not completely useless, though, because its surface charge and the current flowing in it helps in shaping the electric and magnetic fields that will affect the rest of the circuit.)

Moreover what about the perfectly conducting tin can in Haus & Melcher's example? Isn't it connecting the top of the rod with the outer perimeter of the washer? Is there a current flowing there? Is there any power flowing in there? From rod to washer? Let's unfold the geometry, and see what happens when the zero potential reference is placed somewhere else:


fig nut-washer circuit currents and equivalent circuit

So, is energy flowing through the conductor? Using the phi J representation it looks like the answer depends on where you set the zero for the potential:


fig nutwasher for three cases

We can see the inconsistencies of this representation of power flow by considering a single resistor with one side directly attached to the battery


fig one resistor two positions -
power flows in the conductor only if the battery is before the resistor?

what does these say about the way power go from the battery to the resistor? In one case the conductor is bringing power, in the other is does not? And if we add a conductor on the other side as well, one conductor is bringing power to the resistor and the other one doesn't? Does it reverse if we reverse the polarity?


fig one resistor two polarities - power flow alternates between the top and bottom conductors?

And if we call the battery terminals +V/2 and -V/2, power flows into the load from both conductors?
This representation of energy flow is as undetermined as the value of potential.

5)  Are all representations doomed to fail? Possibly. After all, every author warns the reader about only considering the results of the integration over closed surfaces. But we know that in the case of antennas, the energy does flow into space. Where does it stop to be in the space between conductors and starts hiding inside conductors (if ever)? When dE/dt becomes significant? What exactly makes the energy hide into the conductors?

Let's start with an EM beam at very high frequency, such as a laser beam. Is the energy in the space occupied by the beam? I guess it is. Let's lower the frequency and consider an RF antenna beam: is the energy in the space? I guess it still is.


fig antenna beam animation in space
source: sudonull

Lower it a little more and look at a transmission line feeding an antenna. I will add a resistor to steal some of the energy. Is there energy present in the space occupied by a beam exiting an antenna? If the answer to that question is yes, I would say that there must also be energy in the space between the conductors of the transmission line feeding the antenna.


fig animation from transmission line to free space

Now, keep lowering the frequency. The fields of a single 'cell' are basically following the same configuration, but the 'cells' gets longer and longer.




fig lowering the frequency

We will eventually get to a point where we no longer have appreciable radiation and the pattern gets stationary. Is the energy still in the space between wires as the frequency gets lower and lower?


fig transmission line from LF to DC - no radiation, just a fringe effect

When does the energy cease to be in the space between the conductors? At 1Hz? At 0.01 Hz? And at 0.00001 Hz? At DC (meaning from bigbang to bigcrunch)?

6)  Does the Poynting vector have a meaning when we do not have waves?
When Panofsky and Phillips, a book I respect and revere, consider the energy balance in the quasi-static case, they neglect the contribute of the ExH term because, they say, it goes to zero at least as 1/r^5.
But (and this is my thought) this dependency - which is true in the quasistatic state -  is relevant when... r is big. Near the sources, near the wires, with all their surface charge and conduction currents, ExH is usually not negligible. Case in point, in a long cylindrical circuit the magnetic field is approximately constant inside the cylinder, so ExH goes approx as E.
If we enclose our circuit in a bubble and look at the bubble from far away, yes, we will not see any EM energy coming out of our bubble - no diverging contribute of ExH, so to speak. But this does not imply there is no ExH transfer of energy in the circuit's guts.


Appendix
A philosopher might argue that the energy is in the charge and current distribution, and not in the space around them. Maybe, but if I have a ton of water at 0 meters altitude on an iron plated planet and no showel, I can hardly say that my water has any usable energy. But if my ton of water sits in a reservoir h meters above the surface, then there's energy. But is it in the water? Or is it in the gravitational field in the space between water and surface? I would say it is in the field of the composite system planet+water, but that's just me.

Note: a discussion of the engineer's perspective on the 'reality' or not of where the energy flows can be found in

    Edward G. Jordan, Keith J. Balmain
    Electromagnetic Waves and Radiating Systems 2e
    1968, Prentice Hall
    p. 169, section 6.02 "Note on the interpretation of ExH"

As a final side note: electric charges add a twist because they carry a significant field with them (much more than a mass particle - due to the difference in strength between gravitational and EM interaction one would need a reservoir the size of a moon to change the gravitational profile at the Earth surface).

Edit: fixed figure positions, specified position of charge between wires, clarified where Panofsky and Phillips consideration ended. Added philosophical appendix

adx:

--- Quote from: SiliconWizard on January 05, 2022, 05:29:22 pm ---Note that in real life, "DC" is more or less a fantasy. We're always dealing with time-varying fields. Even when the frequency is very low. (And anyway, you'll also have some high-frequency content - just with possibly very low amplitude, but not inexistent.) So in the end, it's always a matter of using an approximation that is "good enough" for a given application. There are always a ton of phenomenons that we are neglecting. :popcorn:

--- End quote ---

That was going to be another idea, but the one I posed (oops Freudian for posted) above seemed much better.

I was wondering about the 0.001Hz idea which Sredni has since posted on (with the ExH insight), but I didn't expect anything very interesting to happen down there beyond the fields seeming to 'freeze' at DC. The way people in physics (from some recent reading) tend to deal with DC is kind of a linguistic limit approach applied to experimental reality (even of a numerical investigation), I forget the wording, but something like "as the system stabilises, the result is shown to approach the expected steady state...". They never say it actually is DC if something like this comes up (or just ignore it and assume DC if it doesn't). And things like bandlimiting out noise. I am guessing it is reasonable to assume that RF effects at ULF are negligible compared to at DC, but I don't have the insight of watching the fields and terms sweep 'down to' zero frequency.

So I was also / more wondering about the kind of thing I was going on about at:


--- Quote from: adx on December 10, 2021, 01:49:30 am ---But I have to concede that for the electrical system you [bdunham7] describe, energy does have to be put into those field(s) to make it work, so the DC analysis is a kind of fallacy (in that there is always going to be stored energy which is there and can conceptually be taken from, and refuelled at the other end). This is central to my gripe with Bernoulli's principle and its (I say false) assumption of conservation of energy. The system has to be charged up before it will work, and energy is different for different arrangements. ...

--- End quote ---

Well, that explains it. If the DCs / steady states are different (say for a circuit with the wires 1m then 0.5m apart) - same current, but different history and energy stored in that current from equilibrium (0), then perhaps something in the way the fields are set up then torn down before and after a 'rest' at DC, can help explain the Poynting vector? As something to look at rather than analyse mathematically (eg feeding it with a Tukey window shaped current pulse (cosine with flat top inserted at the top) to watch perhaps the fields settle in between cosine pieces into a kind of holding pattern amidst something that looks like RF).

Long shot.

adx:

--- Quote from: SandyCox on January 05, 2022, 05:31:17 pm ---...
Coming to think of it, the lightbulb requires a flow of charge (current) to heat up its element. Since the power travelling through empty space cannot be converted to a flow of charge, this cannot be the energy that powers the bulb. The energy has to come through the wires.

Since all the energy that leaves the battery is disspiated in the lightbuld there cannot be any energy transfer through open space at DC.

Maybe Dave should confront Veritasium with this argument.

--- End quote ---

I like that argument, but Sredni and I have now suggested / shown that energy is continually being put into and taken from the field in a DC circuit. There is a superposition of time-varying situations going on.

I'd tend to frame it more like; the flow of charge that does the work on the filament is continuous in quantity all the way along the wires, so it can be argued that it is the source of the current (obviously) or magnetic field, and electric field along the distance of the wires (which is extremely low or even 0 in places, but balances itself over the length of the circuit). From force times speed, or voltage times current (same thing, physically), power is carried by the moving charges.

Sounds completely contradictory, but both are true as far as I can see, so it's more for looking for that elusive answer to the Poynting vector at DC. By that I mean the perfection with which the Poynting vector incorporates the magnetic field, to arrive at its bizarre looking but correct result. But I don't use "bizare" idly, it is because it is inexplicable and unproven at any stage in human history, afaik.

Ok, got to do for the night. Wrong timezone / virtual jetlag.

SandyCox:
Thanks’ to Sredni for the detailed explanation. I need some time to draft a proper response.
For now, I would like to point out that the rotating electric and magnetic dipoles do not represent static conditions. The static fields may exert a force on the dipoles. There is no work being done if there is force without motion. As soon as they start rotating the time derivates of the magnetic and/or electric fields are no longer zero.

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