There once appeared an Associated Press report about a group of Europeans who had levitated a live frog in mid-air and also grasshoppers, fish, and plants, and then quoted one person as saying, "...you could levitate a human."

The experiment attracted media interest throughout the world, with many articles appearing about "floating frogs." The remark about the possibility of levitating humans drew lots of mail. One letter from a religious cult offered over a million dollars for the secret.

How did they levitate the frog? Actually, all materials, including you and me and frogs, are slightly magnetic. The response of our bodies to magnetic fields is billions of times weaker than the response of iron and steel, but in the presence of fields much higher than those of common experience, the electrons in every atom in our bodies can alter their motions and produce a small magnetic field opposing the external field. Provided we or the frog are not carrying any iron or steel, the resulting magnetic force is not attractive but repulsive. So if the magnetic field is vertical, the magnetic force can oppose gravity and yield levitation. With a strong enough magnetic field, anti-gravity becomes science fact.

There's also the unsettled question of whether the huge magnetic fields required would have any damaging effects on the human's health. They were quoted as saying that the frog showed no discomfort. I think it's possible that the frog did have some unpleasant sensations, but was either unable or unwilling to communicate them. The reporter apparently made no attempt to interview the frog.

Levitating frogs and fish is largely a stunt, but levitation of objects that are more magnetic can be accomplished with much lower fields. An object floating in mid-air, without contact with other solid objects, can be moved rapidly without friction. There's even a popular toy that will spin in mid-air for several minutes - provided you have the skill and patience to operate it.

I understood as soon as I saw the article how they had levitated the frog..

Read on for the secret levitation formula!

You may have seen the press report about the group of European researchers who levitated a live frog using an intense magnetic field. I'm still not sure why they levitated the frog, but the laws of physics can tell you how they did it. Like the now-standard trick of levitating a magnet above a superconductor (or vice versa), what is needed is an upward repulsive magnetic force capable of balancing the downward force due to gravity, and the origin of that magnetic force is diamagnetism. However, the diamagnetic susceptibility of a superconductor, is -1, while the diamagnetic susceptibility of a frog (and a person) is only about -.00001 So we'll need a much larger field to levitate a frog - and some order-of-magnitude calculations can tell us what we'll need.

The downward gravitational force on the frog per unit volume is rg, where r is the density and g is the acceleration due to gravity. The density of a frog is about that of water, 1 g/cc or 103 kg/m3, and g is approximately 10 m/s2. So to balance the force of gravity, we'll need an upward magnetic force per unit volume of about 104 N/m3.

In a magnetic field B, the magnetic energy of the frog per unit volume will be -moMH=-MB. Magnetization M=cH=cB/mo, and since c=-10-5, and mo is about 10^^6, M=-10B, and the magnetic energy per unit volume -MB will be about 10B2. Of course there will be no magnetic force in a uniform magnetic field. The magnetic force will equal the upward derivative of the magnetic energy, i.e., 10 d(B2)/dx, and this must equal the gravitational force to produce levitation. So we'll need d(B2)/dx=2B(dB/dx) =103T2/m (10T2/cm) to levitate a frog - or a person. Magnetic fields of 10T or more can be produced with superconducting solenoids or copper-wound "Bitter" magnets of the type used in MIT's Magnet Lab (which require megawatts of power and LOTS of cooling water). With B=10T, you'll need a field gradient dB/dx of about 0.5 T/cm. MIT's Bitter magnets have that sort of field gradient over volumes as big as that of a frog, but not over volumes as big as a human, so for now experiments of this kind will be limited to small animals.

Enjoy.