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Topic: current through a superconductor (Read 8754 times) |
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jarls
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Re: current through a superconductor
« Reply #25 on: Jan 16th, 2009, 10:24pm » |
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on Jan 15th, 2009, 12:56am, towr wrote:
Yeah, cause a real battery only has so much power it can produce. It's not a fundamental problem though, it's a practical one. If there was no limit to the battery output, no limit to heat dissipation (to keep the battery/circuit from heating), and probably no limits to some other parameters, then the current would diverge to infinity.
But in practice the battery will fail, the circuit will heat up, the superconductor will lose it's superconductivity, etc. |
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Why would the circuit heat up if there is no resistance? It's just hard for me to conceptualize of even an idealized battery as having the potential to lend out an infinite number of electrons?
on Jan 15th, 2009, 12:56am, towr wrote:
And I wasn't claiming it was. I was claiming that in physics you can have models that produce results contrary to what is possible in reality.
You shouldn't apply a model beyond it scope. And you shouldn't apply ideal laws to imperfect components as if they were ideal. |
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I'm applying laws only to the electrons which constitute the electrical current. Idealized battery or actual battery, electrons will obey ideal laws in identical ways, even if they do not behave identically. I'm idealizing merely the containment of electrons.
It makes me think of a catapult I suppose. One can conceptually create an idealized catapult in which no hinge has friction and all parts are either perfectly rigid or perfectly elastic. The idealized nature of this would have no bearing on the degree to which the projectile would obey ideal physical law. Imagine, I don't know, a pure collection of electrons, a plasma, (somehow contained) constituting the positive terminal. And for the negative terminal a collection of protons (somehow contained and kept stationary). Would this not in effect be an idealized battery?
I am not by any means experienced in this field and I imagine this conjecture may be entirely nonsensical.
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| « Last Edit: Jan 16th, 2009, 10:50pm by jarls » |
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jarls
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Re: current through a superconductor
« Reply #26 on: Jan 16th, 2009, 10:44pm » |
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on Jan 14th, 2009, 12:54am, towr wrote:
Well, given all that, it would be "infinite". In an ideal short circuit, any charge would redistribute instantaneously (if we ignore the theory of relativity for a moment). |
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A charge's redistributing instantaneously would entail that it either travelled some distance at an infinite rate or traversed no distance at all in redistributing. If there had never been any distance between an electron and the negative electrode it would already have been one with it initially and would no longer have any desire (excuse the anthropomorphism) to redistribute. The notion of a charge, in a short, redistributing instantaneously seems to me to be a paradoxical one.
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| « Last Edit: Jan 17th, 2009, 7:41am by jarls » |
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rmsgrey
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Re: current through a superconductor
« Reply #27 on: Jan 17th, 2009, 12:52am » |
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One minor point: in a conventional circuit, electrons start at the negative terminal and move towards the positive one.
As for the original question: in a stable state, an electrical superconductor can no more have a potential difference across it than can a thermal superconductor have a temperature difference across it.
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towr
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Re: current through a superconductor
« Reply #28 on: Jan 17th, 2009, 3:46am » |
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on Jan 16th, 2009, 10:24pm, jarls wrote:| Why would the circuit heat up if there is no resistance? |
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It wouldn't. But such a circuit does not physically exist. It's an idealization, a fiction, a dream, a figment of the imagination of theorists.
Quote:| It's just hard for me to conceptualize of even an idealized battery as having the potential to lend out an infinite number of electrons? |
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That's merely a lack of imagination, a confusion of reality and fiction. The impossible may be allowed in a fictitious world like ideal circuitry. It's not possible for a real battery. But it wouldn't be an ideal battery unless it can do that.
Quote:| I'm applying laws only to the electrons which constitute the electrical current. Idealized battery or actual battery, electrons will obey ideal laws in identical ways, even if they do not behave identically. I'm idealizing merely the containment of electrons. |
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But that's not part of the model.
It's like saying you can't accelerate to infinite speed in the Newtonian model because of relativity theory. But they're different models. Where in I = V*R do you see electrons mentioned? It doesn't talk of containment.
Quote:| Imagine, I don't know, a pure collection of electrons, a plasma, (somehow contained) constituting the positive terminal. And for the negative terminal a collection of protons (somehow contained and kept stationary). Would this not in effect be an idealized battery? |
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No, it would constitute an idealized capacitor. It would quickly be depleted. It's empty as soon as the charge has gone from one terminal to the other.
You need to replace the electrons on the negative terminal as fast as they move away, and remove them as fast on the positive terminal as they arrive. And unless you can do that at infinite speed, you can't have an ideal battery (because it would stop being ideal once the conductor allows a higher transfer rate than the battery has a replenishing rate)
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| « Last Edit: Jan 17th, 2009, 3:49am by towr » |
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towr
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Re: current through a superconductor
« Reply #29 on: Jan 17th, 2009, 4:02am » |
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on Jan 16th, 2009, 10:44pm, jarls wrote:| A charge's redistributing instantaneously would entail that it traversed no distance in redistributing. |
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No circuitry calculation I've ever done has involved "distance".
It would require a much more detailed model of electrical circuits to take such things into account. For the idealized world you can just imagine columns of electrons all taking a step left simultaneously; in that fictional account distance is not an issue. Or perhaps the battery is near-circular and the wire connecting the terminals is near-infinitely short.
We haven't, after all, the dimensions of either. Our model abstracts from such things.
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SMQ
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Re: current through a superconductor
« Reply #30 on: Jan 17th, 2009, 6:20am » |
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on Jan 17th, 2009, 3:46am, towr wrote:| But such a circuit does not physically exist. It's an idealization, a fiction, a dream, a figment of the imagination of theorists. |
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Minor point: such a battery does not physically exist. It's one of those quantum weirdnesses that the resistance of a superconductor (a real-world, physical superconductor, not just an ideal one) is indeed exactly zero. It only holds within certain limits on temperature and applied magnetic fields, but within those limits there is indeed truly no electrical resistance.
Quote:| No circuitry calculation I've ever done has involved "distance". |
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So you haven't worked with antennas or "transmission lines" then, I suppose.  In certain applications and at high frequencies physical dimensions do become important.
I'll try and address some more of jarls' points later.
--SMQ
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towr
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Re: current through a superconductor
« Reply #31 on: Jan 17th, 2009, 6:44am » |
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on Jan 17th, 2009, 6:20am, SMQ wrote:| It only holds within certain limits on temperature and applied magnetic fields, but within those limits there is indeed truly no electrical resistance. |
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But a current through it generates a magnetic field, right? So even if you fold space and avoid a loop (to keep the electrons on a straight line), if the current increases beyond a point the magnetism will affect the superconductor. ?
Quote:| So you haven't worked with antennas or "transmission lines" then, I suppose. |
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Indeed, I haven't. Most of my experience comes from one course at university; there was some high and low-pass filtering, but that's about the most complex we had to deal with.
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jarls
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Re: current through a superconductor
« Reply #32 on: Jan 18th, 2009, 1:24pm » |
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on Jan 17th, 2009, 3:46am, towr wrote:
That's merely a lack of imagination, a confusion of reality and fiction. \ |
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Shall we stray away from attributing disagreement and misunderstanding to one another's short comings?
on Jan 17th, 2009, 3:46am, towr wrote:
But that's not part of the model.
It's like saying you can't accelerate to infinite speed in the Newtonian model because of relativity theory. But they're different models. Where in I = V*R do you see electrons mentioned? It doesn't talk of containment. |
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I=VR does however dictate the behavior of electrons.
Even in Newtonian physics, for body to attain an infinite rate of motion an infinite amount of time would be required.
on Jan 17th, 2009, 3:46am, towr wrote:
No, it would constitute an idealized capacitor. It would quickly be depleted. It's empty as soon as the charge has gone from one terminal to the other.
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If charge at the negative end were to be regained as soon as it was at all lost, an effect at some point A would have an instantaneous effect at some point B. Would this not also entail traversal at some infinite rate? For the time during electron transfer would it not act as an ideal battery?
My premise, which is in question, is that the notion of an idealized battery does not exist as an impossibility on the same plane as the notion of infinite current. Just as a frictionless system does not exist on the same plane of impossibility as the notion of traversal at an infinite rate
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| « Last Edit: Jan 18th, 2009, 1:24pm by jarls » |
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