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They are diamagnetic i believe (so is water' very weakly so. - google for levitating frogs for a laugh.)

Diamagnetic materials create an equal field to what they are exposed to... Causing repulsion. In the case of superconducting, the field generated is very strong and why we can levitate any old magnet over a superconductor.

Levitating a frog (mostly water right?) takes some incredibly strong fields..... Liquid cooled bitter magnets etc....

Side note - rare earth supermagets are toxic. When they shatter, you dont want to ingest any of the bits/dust



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