Magnets

Diamagnetics was discovered by Michael Faraday in 1846, but no one at the time thought that it could lead to any appreciable effects. William Thomson (Lord Kelvin), referring to levitation as the problem of "Mohamet’s coffin," had this to say: "It will
obably be impossible ever to observe this phenomenon, on account of the difficulty of getting a magnet strong enough, and a diamagnetic substance sufficiently light, as the [magnetic] forces are excessively feeble."

Fields strong enough to lift diamagnetic materials became available during the mid-20th century. In 1939, Werner Braunbeck levitated small beads of graphite in a vertical electromagnet. Graphite has the largest ratio c /r known for diamagnetics (8x10-5
m3/g); today, this experiment can be repeated using just a strong permanent magnet, such as one made of neodymium, iron and boron. Leaving aside superconductors (which are ideal diamagnetics), first levitated by Arkadiev in 1947, it took another fifty y
rs to rediscover the possible levitation of conventional, room-temperature materials. In 1991, Eric Beaugnon and Robert Tournier magnetically lifted water and a number of organic substances. They were soon followed by others, who levitated liquid hydrog
and helium and frog eggs. At the same time, Jan Kees Maan rediscovered diamagnetic levitation at the University of Nijmegen, in collaboration with Humberto Carmona and Peter Main of Nottingham University in England. In their experiments, they levitated
ractically everything at hand, from pieces of cheese and pizza to living creatures including frogs and a mouse. Remarkably, the magnetic fields employed in these experiments had already been available already for several decades and, at perhaps half a d
en laboratories in the world, it would have taken only an hour of work to implement room-temperature levitation. Nevertheless, even physicists who used strong magnetic fields every day in their research did not recognize the possibility.

If you were to tell to a child playing with a horseshoe magnet and pieces of iron that his uncle has a much bigger magnet that can lift everything and everybody, the child would probably believe you and might even ask for a ride on the magnet. If a phy
cist were to say such a thing, he or she (armed with knowledge and experience) would probably smile condescendingly. The physicist would know that only a very few materials, such as iron or nickel, are strongly magnetic. The rest of the world’s material
are not; or to be precise, the rest of the world is a billion (109) times less magnetic. This number seems too big to allow common substances (water, for example) to be lifted even by the most powerful magnets. A billionfold increase in magnetic fields
an be found only on neutron stars. In this case, however, knowledge and experience would mislead the physicist: In fact, all materials can be lifted by using magnetic fields that are rather standard these days.
Whether an object will or will not levitate in a magnetic field B is defined by the balance between the magnetic force F = MB and gravity mg = V g is the material density, V is the volume and g = 9.8m/s2. The magnetic moment M = (/ µ0)VB so that F = (/
µ0)BVB = (/2µ0)VB2. Therefore, the vertical field gradient B2 required for levitation has to be larger than 2µ0 g/. Molecular susceptibilities are typically 10-5 for diamagnetics and 10-3 for paramagnetic materials and, since is most often a few g/
cm3, their magnetic levitation requires field gradients 1000 and 10 T2/m, respectively. Taking l = 10cm as a typical size of high-field magnets and B2 B2/l as an estimate of the order of 1 and 10T are sufficient to cause levitation of para- and diama
netics. This result should not come as a surprise because magnetic fields of less than 0.1T can levitate a superconductor (= -1) and, from the formulas above, the magnetic force increases as B2.
Incidentally, this is the most general principle of Nature: whenever one tries to change something settled and quiet, the reaction is always negative (you can easily check out that this principle also applies to the interac
on between you and your siblings). So, according to this principle, the disturbed electrons create their own magnetic field and as a result the atoms behave as little magnetic needles pointing in the direction opposite to the applied field.

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