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Electroboom: How Right IS Veritasium?! Don't Electrons Push Each Other??
Naej:
--- Quote from: Sredni on June 23, 2022, 05:27:34 am ---
--- Quote from: Naej on June 22, 2022, 09:10:57 pm ---So what makes the current go: either you inject electrons from a normal conductor (and you can then close the superconducting loop after if you want),
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Which is what I wrote above: you need a resistor (the finite conductivity conductor).
--- Quote --- or you bring a magnet close.
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And there will not be current or field inside. Basically the current due to the surface charge that kills the field inside is all you get in a superconductor. In classical electrodynamics we can consider an impossible sheet of current of zero thickness (we can also consider infinitesimal charge quantities, if we wish). In the real world, in a real superconductor, the surface current will be confined to a few atom layers. But this is a far cry from stating that there is a current inside. That fraction of a micron is the real world approximation of the zero depth surface sheet.
There is a discussion of the difference between perfect conductors and superconductors in Ramo, Whinnery, VanDuzer (sec. 13.4 Perfect conductors and superconductors, p. 676 on the second edition).
Anyway, I found the links to Lewin's statement of the problem:
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Is there current in power lines? In a 0.1mm thick copper wire carrying 300 MHz current? Or "just on the surface"?
Here you can see that the wires at LHC are 6 µm thick (probably because of manufacturing constraint/resisting mechanical load), so "everywhere" is the surface. https://lhc-machine-outreach.web.cern.ch/components/cable.htm
And yes all this is explained in your book, and essentially any book talking about skin effect. Which is why Lewin acting as if this were an impossible task even for professors/Nobel prize winners is, to say the least, a bit silly.
Sredni:
--- Quote from: rfeecs on June 23, 2022, 07:20:35 pm ---
--- Quote from: Sredni on June 22, 2022, 07:15:36 pm ---...once in the superconducting material they continue 'by inertia'
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Hm. I wonder how they turn a corner. Apparently they aren't like sheep, guided by the field from the surface charge.
Perhaps they are guided by the surface potential or some other quantum mumbo jumbo.
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As I said, superconductors are quantum beasts. (And that's why I avoid using the term superconductor and use instead perfect conductor, or even 'very high conductivity' conductor when I want to ignore losses in the cables).
We can no longer think of electrons as charged marbles. You need to consider the interaction, the scattering, of the electron wave with the periodic potential of the lattice (and then add in some other quantum mumbo jumbo like Cooper pairs and quantization of fields). Even in ordinary conduction - in real copper at ambient temperature - the model of the charged marble breaks down. We say that the resistor gets hot because these marbles hit the lattice ion, but it's incorrect. The energy is transferred by electron-phonon scattering and it's dominated by the level of impurities and dislocations. In both cases the potential of the lattice... follows the lattice.
Things get complicated pretty quickly.
Maybe an oversimplified explanation could be: if the current is bounded to be on the surface - because there could not be a static B field associated with a flowing current inside - then the electrons are bounded to follow the surface.
I prefer perfect conductors that can sustain a static B field inside, so the electrons can still be considered charged marbles (it's a simplification but it allows me to remain in the realm of classical ED). How do they follow the curves?
If we look at a perfect conductor as the limit of a resistive conductor for resistivity ---> 0, there will be an infinitesimal electric field that will make 'em steer.
The case of exactly 0 resistance is some sort of singularity, and it's nothing new either. We can see it in every single circuit where we neglect the resistance of interconnection. it's like asking yourself "how is it possible for current to flow from Vcc to the collector of the transistor if there is no voltage drop between those two points?"
You can avoid the paradox by invoking lumped circuit modeling, where the interconnects have zero dimension, or you can explain it as the limit case for resistance-->0.
Physically, in classical ED, it might be possible (I have to think it through) to explain the steering by considering what happens when the electrons don't steer: excess charge will appear on the surface (where the electrons "go for the tangent") and that charge will exert a force that will prevent other electrons from not following the shape of the conductor. This very fast feedback will constrain all electrons to follow the cable.
Sredni:
--- Quote from: Naej on June 24, 2022, 12:01:41 am ---
Is there current in power lines? In a 0.1mm thick copper wire carrying 300 MHz current?
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Why are you talking about high frequencies? The circuit we are talking about is DC (EDIT: in case we were talking about Derek's). What is the skin depth in copper at DC? What about 1 microhertz? Or even 1 Hz? (EDIT: how fast do you think Lewin's coil is brought into the field?)
--- Quote ---Here you can see that the wires at LHC are 6 µm thick
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Why you people keep turning simplifications into overcomplications?
Both in Derek's and Lewin's problems the term superconductor is used to avoid the unnecessary complication of losses in the cable, in order to focus only on the phenomena of interest. What's next? A thermodynamic analysis on how it is possible to maintain cryogenic temperatures without altering the fields in the coil? Or a discussion of why Derek did not take into account the temperature profile of the atmosphere and the effect of Van Alllen's (or was it Van Halen?) belt when his cable reach halfway to the moon?
Naej:
--- Quote from: Sredni on June 24, 2022, 06:49:24 am ---
--- Quote from: Naej on June 24, 2022, 12:01:41 am ---
Is there current in power lines? In a 0.1mm thick copper wire carrying 300 MHz current?
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Why are you talking about high frequencies? The circuit we are talking about is DC (EDIT: in case we were talking about Derek's). What is the skin depth in copper at DC? What about 1 microhertz? Or even 1 Hz? (EDIT: how fast do you think Lewin's coil is brought into the field?)
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Derek circuit is not at DC (it's a mind trick), the effect he talks about is at ~1m wavelength (and you can see it on the oscilloscope).
The reason why I used 300 Mhz in a 0.1 mm wire is to get a similar ratio between current depth and wire radius in a copper and superconductor wire.
--- Quote from: Sredni on June 24, 2022, 06:49:24 am ---
--- Quote ---Here you can see that the wires at LHC are 6 µm thick
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Why you people keep turning simplifications into overcomplications?
Both in Derek's and Lewin's problems the term superconductor is used to avoid the unnecessary complication of losses in the cable, in order to focus only on the phenomena of interest. What's next? A thermodynamic analysis on how it is possible to maintain cryogenic temperatures without altering the fields in the coil? Or a discussion of why Derek did not take into account the temperature profile of the atmosphere and the effect of Van Alllen's (or was it Van Halen?) belt when his cable reach halfway to the moon?
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Definitely not in Lewin's. He says E=B=0 inside the superconductor, one of the most well-known fact (or "fact") about them.
If Lewin wanted, he could have taken a wire with a 50 cm thick copper wire, or 5 cm steel wire with a more reasonable size so that it works at 1Hz.
It is, after all, a thought experiment.
aetherist:
--- Quote from: Sredni on June 22, 2022, 07:15:36 pm ---
--- Quote from: rfeecs on June 22, 2022, 06:45:53 pm ---
--- Quote from: Sredni on June 22, 2022, 04:53:29 pm ---I was talking about the surface charge: the excess electrons or lack thereof that - along with the original external field generated by the battery - shape the electric field inside the conductor in such a way that it be directed along the conductor axis and will have a magnitude that satisfies Ohm's law in its local form.
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So what happens with a superconducting wire? Presumably the surface charges make the field inside the wire zero. So what makes the current go?
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Ah. Superconductors are quantum beasts. (Well, technically even ordinary conduction requires quantum theory to give quantitative agreement).
If we stay in the realm of classical ED, we can consider a perfect conductor as the limit of a resistive conductor for sigma->infinity. You need an infinitesimally small field to make the electrons move. But it can get tricky. Last year (?) Lewin posted a problem with a superconducting ring in a changing magnetic field. Basically what we call Lewin's ring but without resistors. What will happen? Only two people, among all those who were exposed to the problem (and they included several physics professors to which Lewin had emailed the problem) gave the correct solution. One is a professor in a University in Switzerland (IIRC) and the other is George Hniatuk (he has a youtube channel).
The solution is: no current inside the superconducting ring.
I had it wrong: my initial assumption was that the current would rise so rapidly - being a superconductor - that the small self inductance of the ring would act as a current limiter. Then I saw George Hniatuk's comment (Nope. No current inside) - and knowing how he knows EM - I realized he was right. (Math and Physics are different - in math you can create the induced electric field magically inside the superconductor, in physics you must justify its presence there. How do you place it in? Surface charge will redistribute in such a way as to prevent it from entering the ring).
But this is not the reason I am telling you this. In the video (I will add a link tomorrow, now I need to sleep), or in the comments, Lewin made a very interesting statement. That to initiate a current in a superconducting ring you need... a resistor. You start your magnetic mumbo jumbo with the resistor inserted - and it's the field in the resistor that makes the electron go - once in the superconducting material they continue 'by inertia', and only after the current is established, you switch to a full superconducting ring.
Pretty crazy, uh?
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Komplete krapp. Lewin is an idiot.
My electon electricity is on the surface of the conductor. Game over.
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