# How is stable levitation possible?

This question is with reference to the video in this blog post: http://www.universetoday.com/90183/quantum-levitation-and-the-superconductor/

My question is the following: how is the disc stable in its levitated position?

Specifically, 25 seconds into the video, the exhibitor turns the entire thing upside down, and the disc doesn't fall. This contradicts two intuitive ideas I have:

1. Right-side-up, gravity is counteracting the repulsive effect of the magnet. Upside down, gravity is working with it. Unless there's some adaptation going on somewhere else, shouldn't "gravity switching sides" be enough to tear the disc away from the magnet?

2. I remembered something about "inverse-square" forces not permitting stable equilibria from college physics - sure enough Wikipedia calls it Earnshaw's theorem. I don't see how this is exempt from that rule. I guess I don't understand diamagnetism.

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Any conductive substance, when moved in a magnetic field, will experience eddy currents, causing drag and energy dissipation because the material has resistance to the currents, generating heat. In a superconductor, this effect is on steroids. The drag is so strong it appears to lock the conductor in the field. No? – Mike Dunlavey Oct 22 '11 at 22:01
I understand stable equilibrium to apply to objects under the influence of a single force, like a mass-spring system without the effects of gravity or friction. The stable equilibrium is where the linear force of the spring exerts no force on the mass. Another example is a balanced object. Say I balance a cone on its point on a table. It is in static equilibrium under the influence of gravity (taking a classical approach). So I don't think Earnshaw's theorem applies to this, because the disc is subject to both gravity and the effect of the magnet. – Fingolfin Oct 23 '11 at 0:56
@MikeDunlavey: I think I get your point: it isn't that the disc is repelled by the magnet, it is that the disc doesn't want to move relative to the magnet. Because if it did, there would be huge eddy currents opposing that movement. The fact that there is still some tiny resistance means that the exhibitor can use his hand to move the disc into and out of the field. – Anonymous Oct 23 '11 at 3:26
the researcher in the video from Tel Aviv is very specific that its not magnetic levitation, but quantum locking. – Vineet Menon Oct 23 '11 at 6:32
@Anonymous: That's what I thought, but actually I like FrankH's explanation better. – Mike Dunlavey Oct 23 '11 at 15:18

I tried to add this as a comment, but it is too long so I am making this an answer instead. This is not my text, but the text of one of the commentators on the video:

• "Superconductors are of two types, which are defined by their Meissner effect. One type repels magnetic fields, which will levitate the superconducting object. A type I superconductor becomes a perfect diamagnetic material, which exhibits a magnetization in the opposite direction of an applied magnetic field. The Meissner effect creates a complete diamagnetic material so that no magnetic field lines are present in that material. I doubt this will suspend the object against gravity by putting it on bottom, for the magnetic fields in opposition will impose a force on the superconductor in the same direction as gravity.

There is what might be called an anti-Meissner effect where the superconducting material collimates magnetic flux lines into narrow tubes or vortex fluxes. If the magnetic field at large is not perfectly uniform it takes work to move the object through the magnetic field and so energetically it is favorable to remain in a region with B_in and B_out remains the same. This is the Landau-Ginsburg effect and is found in type II superconductors. I think that this is a case of a type II superconductor."

This sounds right to me and explains what is meant by quantum locking since superconductivity is a macroscopic quantum phenomenon that is effectively locking the magnetic flux into specific tubes in the superconductor. The force that opposes gravity is, of course, magnetic so we are not talking about any kind of new force of nature.

When he uses his hand to move the superconductor, he is using enough force to make the magnetic flux tubes be rearranged but apparently the force of gravity is weak enough such that it cannot rearrange the flux tubes by itself. So I predict that if you added enough weight to the puck, it would fall :)

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Your explanation makes more sense than mine. – Mike Dunlavey Oct 23 '11 at 15:16

There is an easy trick behind this. Look closely at the video, the superconducting disc is levitating above several small magnets. The magnets are placed in a checkerboard configuration:

+ - + - + -

- + - + - +

+ - + - + -

Now draw the magnetic flux lines for this configuration. It will basically look like a lot of rings going in and out of the magnets. With this configuration you can already levitate a small piece of graphite because of the high diamagnetism. With a type 2 superconductor another phenomenon locks the disc above the magnet: As FrankH already mentioned you the flux lines will penetrate the superconducting disc if you force it in this position. Due to small impurities you will have areas in the material that are not superconducting and the flux lines will stick to those areas. This is the energetically most favorable state.

If you try to move the disc these flux lines have to move from the impurity site through the material and create small non-superconducting areas which is energetically unfavorable (you lose the condensation energy in those areas).

The locking of the flux lines can be much stronger than gravity and is already used to levitate trains (Maglev).

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From the wiki link for Maglev: ...EMS systems rely on active electronic stabilization. Such systems constantly measure the bearing distance and adjust the electromagnet current accordingly. All EDS systems are moving systems (no EDS system can levitate the train unless it is in motion). If superconducting magnets are used on a train above a track made out of a permanent magnet, then the train would be locked in to its lateral position on the track. ... This is due to the Meissner effect. --- so it appears that none of the Maglev trains use the Type 2 superconductor technology. – FrankH Nov 2 '11 at 1:46
@FrankH: Yes, there are different suspension systems for Maglev trains. The locking effect of a type 2 superconductor has been used in this prototype train: Supratrans, I am not sure whether it has been used already in big commercial trains. – Alexander Nov 2 '11 at 10:26
@FrankH I think you're grossly misreading that wiki article. Besides, all of the high-Tc superconductors are type-II; any large scale application of type-I SC is usually completely unfeasible, since you need liquid helium cooling. – wsc Dec 1 '11 at 14:54