https://www.lenfisherscience.com/56-the ... ting-frog/
The true story of the levitating frog
by Len Fisher
24 Mar 2015
Mini Stories from Science
When Professor Michael Berry gave a seminar in our department at Bristol on the physics of levitation, the emphasis was all on the physics. And so it should have been, because his profound insight had overturned a belief that physicists had held for more than a hundred years.
The belief was that there was no way for stable magnetic levitation to occur. This result from classical physics was proved mathematically by Samuel Earnshaw in 1842, and is known as Earnshaw’s theorem. Simply put, the theorem says that no object can be held stably by magnetism and gravity alone. So one can imagine Michael’s surprise when he looked in the window of a novelty shop and saw a spinning top hovering lazily above a magnetized base, oblivious to Earnshaw’s theorem and suspended solely by magnetic repulsion.
If one magnet is suspended above another, with their same poles facing each other (say North-to-North) and hence repelling, the top magnet will just flip over unless it is spinning, and hence stabilized gyroscopically. But Earnshaw’s theorem (which also applies to arrays of magnets) says that the upper magnet will not hover in the same position, but will always have a tendency to slip off sideways.
This is what the spinning top (known as a levitron) did not do. As an old chief of mine used to say, fact is the death of hypothesis, and Michael was able to account for this new fact when he proved that, while Earnshaw’s theorem remains correct for non-rotating objects, this is not so for spinning objects, which can stay hovering indefinitely within a narrow range of conditions for magnetic strength, weight, and rate of spinning.
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