# Levitation and Stability

Q:
with just three magnets, can you make one of the magnets float? if so, will you show me?
- chris
ny
A:
Some questions have tricky answers, but not this one. The answer is NO. A theorem (Earnshaw’s theorem) shows that any collection of static classical objects interacting via electricity, magnetism, and gravity will not be in stable equilibrium.That means none of them will be stably supported out of contact with the others. That applies even if you use many objects, not just three.
You can get stable equilibria if non-classical quantum effects are important. These become important whenever objects are in contact, so Earnshaw did not prove that you can’t build a house. They can also cause another non-classical effect, diamagnetism, in which objects actually are repelled from strong magnetic fields. This becomes a strong effect for superconductors, which are often used for little levitation demonstrations.

Mike W

Another way to escape the conclusions of Earnshaw’s theorem is to allow the magnets to be non-static. One example of levitation not using a superconductor is to make a many-turn loop of wire with an alternating current in it. This object will float above a conducting metallic plate for a similar reason to why a magnet will float above a superconductor -- currents flowing in the plate will create magnetic fields which oppose the external one applied from the loop of wire. These will eventually die away resistively for ordinary metals (but not superconductors), and so the oscillating magnetic field is necessary to keep the coil levitated.

You can also arrange stable levitation with a feedback mechanism, which rearranges the magnets or redirects current through electromagnets so that when the levitated object begins to slip and fall, the fields are changed to push it back up again. Some magnetically levitated train designs rely on this kind of mechanism to keep the train properly levitated with respect to the rails at all times.

Tom J.

(published on 10/22/2007)

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