According to Steve Gourlay, the head of the Lawrence Berkeley National Lab’s Superconducting Magnet Group, superconductors have the ability to freeze the flux lines of the magnetic field. Once a high-temperature superconductor is too hot to work, the magnetic fields can pass through it without a hitch.
However, once you cool the superconductor to such an extent, that it ‘starts working’; the magnetic field lines that were passing through it will be caught in a mesh of sorts.
This will leave the superconductor attached to the magnetic field in a particular location. As long as you keep the superconductor cold enough, it’ll stay floating above the magnet while its eddy currents fight gravity to a draw.
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