Although the following video is illustrative of the Meissner effect, it is not a true Meissner effect.
These experiments are conducted on cuprates, which are type II superconductors, with quite weak first critical fields, Bc1(typically between 10 and 100 G), and very high second critical fields, Bc2(over 20 T). The superconducting disks used in these videos have very weak pinning; the vortices are free to move out of the sample if they are too numerous compared with the ideal compromise determined by the temperature and the external magnetic field. Hence, the experiment is not a pure Meissner effect. The magnetic field created by the magnet exceeds Bc1.
The sample is not completely diamagnetic, only partially. This partial diamagnetism may be strong enough to lift the magnet if the latter is not too heavy!. Although pinning is weak in these samples, it is not equal to zero. If you move the disk with tweezers, the levitating magnet above will follow the movement. This proves that there is not only a repulsive force, but also a weak “pinning force” corresponding to the (weak) pinning of the vortices. If there was only a repulsive force, the magnet levitation over the flat disk would not be stable; the magnet would slide to the side and fall. This is the reason why this experiment conducted with a type I superconductor (e.g. lead where only the Meissner effect can exist) requires the magnet to levitate over a bowl rather than a flat disk, to stabilize the levitation and prevent the sample from sliding to the side.
However, although we made these videos using cuprates, they are still illustrative of the Meissner effect, since they show the magnet levitating even though the vortices go through the sample and lower the actual diamagnetism of the disk. Paradoxically, the presence of these vortices is essential to the magnet stability!
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