General > General Technical Chat
"Veritasium" (YT) - "The Big Misconception About Electricity" ?
Sredni:
--- Quote from: SandyCox on January 03, 2022, 09:05:49 am ---Let’s look at Haus and Melcher’s example 11.3.1 in more detail. We look at the example from the point of view of conservation of energy. We can calculate the power entering the washer from the voltage source. We can also calculate the power entering the rod from the voltage source.
We then use Poynting’s theorem to calculate the power that is dissipated in the rod and the power that is dissipated in the washer. It all ads up correctly. All the power that is delivered by the voltage source to the rod is dissipated in the rod. All the power that is delivered by the voltage source to the washer is dissipated in the washer.
According to our misinterpretation of the Poynting vector, Fig 11.3.1 leads to the conclusion that power is being transferred from the washer to the rod through region (a). This simply isn’t happening.
--- End quote ---
We can say the same for the three parallel resistors: in the middle section we see lines of Poynting field coming out of the first resistor and getting into the second one. The first resistor is in the way of power transfer to the second resistor but is not the source of the energy (no more than the empty space between battery and first resistor is). Didn't Haus and Melcher warn the reader about the dangers of ascribing meaning to S evaluated at a point, rather than integrated over a closed surface?
And besides, you say
"All the power that is delivered by the voltage source to the rod is dissipated in the rod. All the power that is delivered by the voltage source to the washer is dissipated in the washer."
The same happens with the parallel resistors: all the power delivered to the first resistor - which you can compute by integrating over a closed surface containing it - is dissipated in the first resistor (where else?)
In the convoluted geometry of H&M cylinder, washer and rod share the power delivered by the battery. Change the resistivity of the material and you should be able to have one glow red hot, while the other stays cool.
Sredni:
--- Quote from: bdunham7 on January 03, 2022, 05:44:20 am ---
--- Quote from: Sredni on January 02, 2022, 02:12:20 pm ---Is the fact that the first resistor in the above figure is getting all the field lines coming from the battery what you find of concern?
--- End quote ---
I downloaded that and was unable to get it to run (yes I read the instructions) and apparently you haven't either since you just posted the sample shot.
--- End quote ---
Yes, I downloaded it as well and got an error at runtime. But my laptop is so old that almost nothing works anymore. I am relieved to see I am not the only one not being able to run it.
--- Quote --- I'm not sure that it is complete or accurate, but maybe it doesn't matter. What happens if you disconnect the first resistor right at the two ends?
--- End quote ---
The total power deliver by the battery will be less, and the Poynting field lines will go through the region of space where the disconnected resistor is as if it were empty space.
Also, I see in another post someone - maybe you - noticed the absence of lines outside the circuit. This is a consequence of the 2D simplification to make computations easier. The circuit is a 2D slice of an infinite cylindrical circuit with infinitely long linear battery and infinitely long linear resistor. This will make the magnetic field much like that of an infinite solenoid: exactly zero outside and uniformly constant inside. This is why the Poynting field lines are directed as the electric field equipotentials.
You might argue that this is an unphysical situation, but it's at least a very reasonable approximation of finite length cylindrical circuits (much in the same way infinitely long solenoids are a reasonable approximation of finite length real-life solenoids). The difference with respect to a flat circuit in 3D is the magnetic field decreasing with distance from the conductor and its presence outside. The Poynting field will be present all around the conductors and will be stronger near them. Still, it will be in space between them.
SandyCox:
--- Quote from: Sredni on January 03, 2022, 10:26:39 am ---
--- Quote from: SandyCox on January 03, 2022, 09:05:49 am ---Let’s look at Haus and Melcher’s example 11.3.1 in more detail. We look at the example from the point of view of conservation of energy. We can calculate the power entering the washer from the voltage source. We can also calculate the power entering the rod from the voltage source.
We then use Poynting’s theorem to calculate the power that is dissipated in the rod and the power that is dissipated in the washer. It all ads up correctly. All the power that is delivered by the voltage source to the rod is dissipated in the rod. All the power that is delivered by the voltage source to the washer is dissipated in the washer.
According to our misinterpretation of the Poynting vector, Fig 11.3.1 leads to the conclusion that power is being transferred from the washer to the rod through region (a). This simply isn’t happening.
--- End quote ---
We can say the same for the three parallel resistors: in the middle section we see lines of Poynting field coming out of the first resistor and getting into the second one. The first resistor is in the way of power transfer to the second resistor but is not the source of the energy (no more than the empty space between battery and first resistor is). Didn't Haus and Melcher warn the reader about the dangers of ascribing meaning to S evaluated at a point, rather than integrated over a closed surface?
And besides, you say
"All the power that is delivered by the voltage source to the rod is dissipated in the rod. All the power that is delivered by the voltage source to the washer is dissipated in the washer."
The same happens with the parallel resistors: all the power delivered to the first resistor - which you can compute by integrating over a closed surface containing it - is dissipated in the first resistor (where else?)
In the convoluted geometry of H&M cylinder, washer and rod share the power delivered by the battery. Change the resistivity of the material and you should be able to have one glow red hot, while the other stays cool.
--- End quote ---
I fully agree with everything you are saying. We are making the same point.
You are just applying Poynting’s theorem. Poynting’s theorem is absolutely correct.
The point I’m trying to make is indeed about the dangers of ascribing meaning to S evaluated at a point. People have incorrectly come the conclusion that the Poynting vector points to some kind of conduit through which electromagnetic energy is transferred. Ascribing meaning to the Poynting vector at a point leads us to the wrong conclusion, as shown by Fig. 11.3.1.
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?
Sredni:
--- 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.
adx:
--- Quote from: SandyCox on January 02, 2022, 05:52:39 pm ---... It makes my point even clearer. ...
--- End quote ---
Good point.
I'm wholly unsatisfied with that diagram as any sort of level-headed description for where the power "really" flows. It's warped and wrong-looking. This is not just intuition:
You've got a single-valued proxy for "current flowing around this loop", and a(n electric) field gradient which basically says "this voltage between these wires divides over this space in this way". That is to say, exactly(?) what I was saying earlier in that the power flow is a combination of moving charge carriers and potential difference. Except to map this out over space requires some fast and fancy guesswork. Kind of a geometrical mean between apples and oranges - which is what this diagram is. But that's not beyond someone with no appreciation of concepts like induction, capacitance, speed of light, EM etc to draw it up. All it requires is an extremely simplistic grasp on magnetics (not even any 1/r law), P= V*I, and an ability to graphically divide voltage up into equipotential lines.
So there's 2 problems for the statement that it is the true physical nature of power flow at DC:
1/ The only 'evidence' supporting its physical truth is that it works at AC, with induction, where a location for fields induced by said induction is defined by Maxwell's equations, leading to an easily testable idea of where the power is as it tries to travel over space. (And perhaps the fact that steady state doesn't really exist.) But in the situation that it looks wrong and warped as a model at DC, that's not enough to make it acceptable.
2/ My first guess to resolve the conundrum of where power flows if it must partly go as a difference between two paths of movement, gives the same result but as a self-fulfilling image of "the energy is here" based on rather uneducated guesswork. That's even less satisfying.
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