Magnet hovering and spinning over a cooled object

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Yoni
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There is an amazing physics demonstration I saw on the web of how a magnet is hovering over a cooled object. Seemingly the magnet hovers (and spins slowly) over a single spot. However, while forcing the magnet out of it's equilibrium it is possible to place it almost anywhere near the cooled object, and it retrieves its equilibrium state over the new spot!

This whole phenomenon is a mystery to me... What is the cooled object? How does this happen? And how can there exist multiple possible equilibriums?
 
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The cooled object is a high-temperature superconductor. As the magnet is moved around and whatnot, the emf generated in the superconductor because of Faraday's Law due to the change in flux must remain 0 because you cannot have an electric field inside a superconductor. Since the resistance is 0, you can have any current flow within the superconductor, causing eddy currents from the superconductor. These eddy currents cause the change in flux to always be zero, and that results in no net magnetic field in the superconductor. This arrangement causes magnetic pressure between the magnet and the superconductor.
 
Thank you for the explanation.
Is the superconductor created by a simple metal? Or was it a magnetized?
I still don't understand how exatly this "magnetic pressure" is able to create multiple equilibriums, if this was indeed what I saw.
 
Superconductivity just means "zero resistance" and no interior magnetic field. Only certain materials can do this, and only at very very low temperatures, close to absolute zero.
The reason the magnet levitates is as Snazzy said. Basically, in order to keep the properties of a superconductor, a changing current will be generated, making an magnetic field equal to that of the magnet.

This isn't easy or cheap to reproduce, if that's what you're looking to do!

Alexandre Colavin
 
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However, different superconducting materials are being found, and we have reached a point where we can produce this effect merely by using liquid nitrogen.