This levitation effect is explained by the Meissner effect, which describes how, when a material makes the transition from its normal to its superconducting state, it actively excludes magnetic fields from its interior, leaving only a thin layer on its surface.
When a material is in its superconducting state — which involves very low temperatures — it is strongly diamagnetic. This means that when a magnetic field is externally applied, it will create an equally opposing magnetic field, locking it in place.
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