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Absurdity of superconductivity's London Equations by goran d on 11 Apr, 2017 12:32
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There is something bothering me about the London Equations used in superconductivity. The first equation is "derived" by using the Lorentz force with the magnetic component discarded. The second one is derived from the first one. But this is an absurd assumption. If it were true, then, if we attach a magnet to a piece of superconductor, the whole system will accelerate in the direction of the magnet due to lack of magnetic force on the currents in the superconductor.
The only resolution of this problem I can think of is if there is an extra electric field generated in the superconductor, equal to minus the cross product of v and B. That way, the magnetic force will be transferred on the protons, and the absurd situation is resolved. This field will violate Maxwell's Equations.
However, in this case, if we also charge the superconductor, the extra electric field will act on the surplus charge and produce net force. This force will be very small under ordinary conditions, as the ratio of the charge to the total cooper pair charge in the layer of current is very small. However, under small scale, the dielectric strength of materials increase a lot. Or it could use diamond dielectric to increase the allowed charge. -
#1 by goran d on 11 Apr, 2017 13:06
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Oh, and if we modify the extra E-field equation a bit, to be constant times the cross product of velocity and curl of velocity of the cooper pairs, that can explain the claims made by Eugene Podkletnov.
When testing in air, the potential of the Earth would create a charge on the super conductive disc, and it would produce a net force. However, in a vacuum chamber, the walls of the chamber will shield the Earth's E-field and there would be no charge on the disc. Hence no force in vacuum chamber. -
#2 by whitelancer64 on 11 Apr, 2017 13:59
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"If it were true, then, if we attach a magnet to a piece of superconductor, the whole system will accelerate in the direction of the magnet due to lack of magnetic force on the currents in the superconductor."
Sounds like you've got an experiment to do. -
#3 by meberbs on 11 Apr, 2017 15:07
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The first equation is "derived" by using the Lorentz force with the magnetic component discarded.
I am not sure where you got this idea from, I think you should read the wiki article https://en.wikipedia.org/wiki/London_equations which has a good description of these equations including "While it is important to note that the above equations cannot be formally derived..."
The first equation doesn't include a B field term because if you think about it, while the B field is applying a force to the individual electrons, in steady state, this force does not change the current density, just keeps the electrons moving in the same circles. (It also applies in not steady state, but is more difficult to see, since the changing magnetic field produces an electric field that accelerates the electrons)But this is an absurd assumption. If it were true, then, if we attach a magnet to a piece of superconductor, the whole system will accelerate in the direction of the magnet due to lack of magnetic force on the currents in the superconductor.
The equations are an empirical description (like Ohm's law) of how the currents behave under the applied fields. Neither equation actually describes the net force on the superconductor. Actually calculating the force on the superconductor from the fields is difficult, as it usually is for calculating the force between 2 magnets, and if you did so you would find no such self accelerating device. -
#4 by goran d on 07 May, 2017 16:48
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I'm sorry, but the second London equation is contradictory. It implies that a current in a wire is in the opposite direction to itself. It always gives direction to the current which will reduce the magnetic field, but in a super-conducting wire, the current doesn't reduce the magnetic field, it causes it.
In the wire, the curl of the current will be in the opposite direction to the one predicted by the second London equation. -
#5 by RotoSequence on 07 May, 2017 16:58
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I'm sorry, but the second London equation is contradictory. It implies that a current in a wire is in the opposite direction to itself. It always gives direction to the current which will reduce the magnetic field, but in a super-conducting wire, the current doesn't reduce the magnetic field, it causes it.
In the wire, the curl of the current will be in the opposite direction to the one predicted by the second London equation.
I don't suppose you've had access to superconducting magnets to perform experiments and record observations to confirm or refute this hypothesis yourself? -
#6 by meberbs on 07 May, 2017 18:12
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I'm sorry, but the second London equation is contradictory. It implies that a current in a wire is in the opposite direction to itself. It always gives direction to the current which will reduce the magnetic field, but in a super-conducting wire, the current doesn't reduce the magnetic field, it causes it.
First some background on conductors you seem to have forgotten: in a conductor current tends to flow on the surface, rather than through the bulk. In the case that there is only current flowing straight on the surface, then there is no magnetic field inside the conductor. This is easy to see from the integral version of Ampere's law, because any loop drawn inside of the conductor encloses 0 current.
In the wire, the curl of the current will be in the opposite direction to the one predicted by the second London equation.
With current flowing straight along a wire doesn't have a curl, and their is no magnetic field inside, so the equations should seem consistent at a glance.
The London equations are better than that though, because they properly account for the finite current thickness. I have attached a sketch zoomed in near the surface of a superconducting wire showing the curl of the current due to the gradient of the current as the current strength decreases deeper in the superconductor, and the remaining magnetic field inside the superconductor, which is aligned with the curl as expected. I use thickness of lines to indicate magnitude. Blue for magnetic field, green for current, circles with dots mean "out of page", circles with x's mean into page. Circles with arrows on them illustrate local rotation that is measured by curl.
It seems pretty clear that everything is consistent. The curl of the current is in the same direction as the magnetic field inside the conductor.
While I appreciate the chance to practice my electrodynamics, I don't know why you are so insistent on trying to find flaws in equations that work very well both theoretically and when compared to experiment.
Edit: I made 2 mistakes above that happen to cancel out, so the conclusion that London's equations are valid remains correct.
Mistake 1: I forgot about the negative sign in the relevant London's equation.
Mistake 2: When figuring out the direction of the magnetic field inside the superconductor I got lost in the micro view and forgot about the big picture of how the fields from elsewhere in the wire also contribute. My mistake should have been obvious to me, since I had a finite current density reversing the direction of the magnetic field. To get the correct direction, I should have pictured drawing concentric circles inside the wire, and each larger circle contains more current, so field strength get stronger closer to the outside of the conductor, and is always in the same direction as the external field.
The one mistake in the drawings below is that the direction labelled for the net magnetic field inside the conductor is wrong, it should be pointed opposite to the curl of the current as London's equations predict.
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#7 by goran d on 07 May, 2017 18:25
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It seems pretty clear that everything is consistent. The curl of the current is in the same direction as the magnetic field inside the conductor.
Ahh, but in the second London equation the curl of the current is in the opposite direction to the magnetic field. -
#8 by gospacex on 07 May, 2017 18:40
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www.physicsforums.com might have more physicists to help you with your question
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#9 by meberbs on 07 May, 2017 19:04
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See above, I noticed 2 mistakes and corrected before I saw your post.
It seems pretty clear that everything is consistent. The curl of the current is in the same direction as the magnetic field inside the conductor.
Ahh, but in the second London equation the curl of the current is in the opposite direction to the magnetic field.