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 "Moham ets coffin," had this to say: "It will ob ably 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-20 th century. In 1939, Werner Braun beck levitated small beads of graphite in a vertical electromagnet. Graphite has the largest ratio c /r known for diamagnetics (810-5 m 3/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 Tour nier magnetically lifted water and a number of organic substances.

They were soon followed by others, who levitated liquid hydro g 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 ever 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 worlds 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 billion fold 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. 8 m / s 2. The magnetic moment M = (/ u 0) VB so that F = (/ u 0) VB = (/2 u 0) VB 2. Therefore, the vertical field gradient B 2 required for levitation has to be larger than 2 u 0 g/. Molecular susceptibilities are typically 10-5 for diamagnetics and 10-3 for paramagnetic materials and, since is most often a few g/ cm 3, their magnetic levitation requires field gradients ~1000 and 10 T 2/m, respectively.

Taking l = 10 cm as a typical size of high-field magnets and B 2 ~ B 2/l as an estimate of the order of 1 and 10 T are sufficient to cause levitation of para- and diam a net ics. This result should not come as a surprise because magnetic fields of less than 0. 1 T can levitate a superconductor ( = -1) and, from the formulas above, the magnetic force increases as B 2. 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. All the atoms inside the frog, act as very small magnets creating a field of about 2 Gauss (although very small, such a field can still be detected by a compass).

One may say that the frog is now built up of these tiny magnets all of which are repelled y the large magnet. The force, which is directed upwards, appears to be strong enough to compensate the force of gravity (directed downwards) that also acts on every single atom of the frog. So, the frogs atoms do not feel any force at all and the frog loans as if it were in a spacecraft. ) There are a few materials (such as iron) whose atoms are a bit crazy and love to be in a magnetic field. Their magnetic needles are oriented in the same direction. But those are exceptions from the general rule.

A hazelnut, a frog, and a globule of water all hovering, or levitating, have to be in a in a magnetic field of at least 10 T. This field strength is only several times more than that of existing permanent magnets (about 1. 5 T) and only 100 times or so roger than that of a typical refrigerator magnet. One need just open a textbook on magnetism to realize that such fields can lift "nonmagnetic" materials.

Indeed, the magnetic force acting on a material of volume V with susceptibility c in a magnetic f ld B is F = (M) B where the magnetic moment M = (c /m 0) VB. This force should compensate the gravitational force mg = r Vg (r is the material density and g is the gravitational acceleration) and, hence, the vertical field gradient B 2 required for lift g has to be greater than 2 m 0 g (r /c) (here we use "lifting" to distinguish it from "levitation", which means stable floating). Just because an object can levitate does not mean that it will when placed in a strong enough magnetic field. The right conditions are surprisingly subtle; for instance, even an increase of only a few percent in magnetic field will normally destabilize levitation and cause the object to fall.

A diamagnetic object can levitate only close to an inflection point of the vertical component of the magnetic field, where d 2 BZ/dz 2 = 0. Note that this is a purely geometrical condition, which does not depend on t field strength. The spatial extent of the region of stable levitation is typically a small fraction of the magnets size - just 2 centimeters for a half-meter Bitter magnet, for example. Accordingly, the field strength must be carefully adjusted to com n sate for gravity at that particular point. If the field is slightly weaker than required, the object falls; if stronger, the field is horizontally unstable and only the magnet walls stop the object from moving sideways and then falling. A gentle touch or airflow can easily destroy the levitation.

Those who have tried to levitate high-temperature superconductors would probably raise their eyebrows, since they encounter no problems. However, super-conducting levitation takes advantage o magnetic flux lines being pinned inside a superconductor; this is what makes floating superconductors such a familiar sight. Eliminate pinning, and once again careful adjustments of both spatial position and field strength are required. The idea of diamagnetic levitation is so attractive that, when first learning about it, experimental physicists naturally start thinking - if only for a brief moment - about employing the effect in their particular research.

Indeed, super-conducting ma ets with a room-temperature bore are relatively cheap these days, -a reasonable, basic setup costs about $ 100, 000 - making access to the levitation affordable even for individual research groups. Watching a levitating water drop in a magnet, one inevitably starts thinking about studying weightless fluid dynamics, not on board a space shuttle but simply in a laboratory. Container less crystal growth, also a frequent subject of space research, is other obvious application to consider. Or take, for example, diamagnetic ally suspended gyroscopes. In our own recent experiment, we could observe Earths rotation using a small plastic ball levitated in a magnet and spun by a laser beam. Not a great ach v ement in itself, but already those first attempt has shown error drifts of just 0.

1% of Earths rotation, a record low for any type of gyroscope. Magnetic micro-gravity seems to work well even for complex biological systems. Several groups of biophysicists, - such as those led by James Valles of Brown University, Karl Hasenstein of the University of Southwestern Louisiana and Markus Braun of the niversity of Bonn (Germany) -, have already begun studies of plant and animal responses to such magnetically simulated micro-gravity. Biological systems are astonishingly homogeneous with respect to diamagnetic levitation: Seemingly diverse components ch as water, tissues, bones and blood differ in their values of c /r by only several percent, which implies that gravity is compensated to better than 0. 1 g throughout a complex living organism.

Further, even if paramagnetic molecules and ions are presen as in blood, they contribute only to the average susceptibility; their strong response to the field is smeared out by temperature (mBB 315.