No levity when we levitate our frog

October 13, 2000

A dubious honour was awardedto Sir Michael Berry for his efforts to suspend an animalin midair, but he is adamant of its scientific value

Sir Michael Berry of the physics department at Bristol University last week won an IgNobel Prize for 2000, keeping prestigious company with the Royal Navy (Peace Prize) and a group of investigators concerned with toilet collapse in Glasgow (health). He argues that despite this company, his award for magnetic levitation of frogs, shared with Andrey Geim of Nijmegen University, is for serious science.

The flying frog was Andrey Geim's experiment. I was told about it after giving a lecture on the physics of the levitron - a toy in which a magnetised spinning-top floats above a magnetised base. It seemed that the flying frog and the floating top ought to depend on similar physical principles, so I got in touch with Andrey. Then we worked together to extend to the frog the explanation I had found for the levitron.

It is surprising at first to see the frog and the top suspended in midair, in apparent defiance of gravity. They are supported by the force of magnetism. For the frog, the force comes from an electromagnet; for the top, the source is a magnetised metal slab. These powerful magnets push upwards on the frog and the top, because they are magnets too (weak ones). The magnetic force exactly balances gravity, so the top and the frog are in equilibrium and can float - there is no net force on them. A slight difference is that the top is intrinsically magnetised - it is a permanent magnet - while the frog is intrinsically non-magnetic but becomes magnetised by the field of the electromagnet - this is "induced diamagnetism".

Most substances are diamagnetic, and Andrey was able to levitate a variety of objects, including drops of water and hazelnuts. Magnetic levitation is not antigravity - gravity is not eliminated by the magnetic force, but counterbalanced by it. When you are standing, the downward force of gravity is balanced by an upward force on the soles of your feet from the atoms in the ground, that stops you falling to the centre of the earth. But the force on your feet is a short-range force, so it only acts when your feet touch the ground.

Magnetism is a long-range force (like gravity), so the top and the frog can be suspended without touching anything. The magnetic field that holds up the frog is a few times stronger than the fields used medically, in magnetic resonance imaging. In principle, a person could be magnetically levitated, too - like frogs, we are mostly water. The field would not have to be stronger, but would have to fill the much larger volume of a person, and that has not been achieved yet. I have no reason to believe that such levitation would be a harmful or painful , but of course nobody can be sure. Nevertheless, I would volunteer to be the first levitatee.

To be levitated in this way could be an interesting experience. When we are standing, the force that holds us up acts only on our feet, and we feel the upward push. But with magnetic levitation the gravity-compensating force is approximately uniform over the whole body, like gravity itself, so magnetic levitation would be more like the weightlessness experienced by astronauts in space.

But there is a difference: the diamagnetism of the body is not uniform - tissues, bone, blood and so on have different magnetic properties - so we would feel slight pullings and pushes over the body. If the magnetic force on flesh is greater than that on bone, it would be as though we were held up by our flesh, with our bones hanging down - a bizarre reversal of the usual situation, and possibly the basis for a type of face-lift. I know no other experience to compare this with, and so have no way to anticipate what it would feel like.

The tricky part of the physics is to understand why the equilibrium of the top and the frog is stable - that is, why the objects remain suspended. Most physicists would - mistakenly - expect the top and the frog to slip sideways out of the field and fall (an analogy is the instability of a pencil balancing on its point). This wrong expectation is based on a theorem proved by Samuel Earnshaw in 1842: no stationary object can be held stably by magnetism and gravity alone. But the flotation is stable, notwithstanding Earnshaw's theorem, because the top and the frog are not stationary. For the top this is obvious, because it is spinning - as it must be to prevent it from overturning and being attracted, rather than repelled, by the magnetised slab. In the case of the frog, the counterpart of spin is the circulation of electrons in the creature's atoms. These are small effects, but they mean that Earnshaw's theorem does not strictly apply, and this opens the possibility that the equlibrium could be stable.

Calculations involving the precise pattern of the magnetic field show that there are very small regions - just a few millimetres in extent - where the frog and the top can be stable. The trick is to get the forces to balance in these regions - if you get it wrong, the top and frog will fall. Getting the balance right involves fine adjustments: of the strength of the magnetic field that holds up the frog and of the weight of the top. The theory of this sort of magnetic levitation was anticipated by other people. In 1960, Vladimirskii gave what amounts to the theory of the levitated top, but the spinning magnets he was thinking of were subatomic particles such as neutrons. And lectures given by Lord Kelvin in the 1850s give a strong hint that he had worked out the theory underlying the frog's levitation - but he thought diamagnetism was so weak that magnetic fields large enough to cause levitation could never be achieved.

Both Andrey and I spend most of our time on other physics. In his case, the magnetism of solids; for me, quantum theory and optics.

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