The question as it appears in the 12/12 edition of Specs & Techs from GlobalSpec:
You're having a discussion at lunch with your friend, and she tells you that she can make one magnet levitate in freespace above another magnet. You tell her that's impossible, citing Earnshaw's Theorem as your proof. Who's right?
Update (01/02/07 9:12 AM): And the Answer is....
Unfortunately, you lose this one, as your friend demonstrates the next day when you walk into her office and she shows you a small top, spinning happily in midair about two inches above a circular base.
Relax. There's no need to lose faith in your college E&M professor. Earnshaw's Theorem states that there is no static configuration of permanent magnets that allows levitation. The operative word in this case is static. The system your friend has just demonstrated for you is dynamic, because one of the magnets is spinning, so Earnshaw doesn't apply to this system. The stability region is bounded by a pretty narrow range of spin speeds, height, weight of the top, and the slightly offvertical alignment of the base magnet's field. With some careful adjustment the top will levitate for several minutes, until its rotation slows enough that there is no longer enough gyroscopic action to keep it stable. At that point Earnshaw takes over and the top falls.
Spin stabilized levitation was first demonstrated by inventor Roy Harrigan. More indepth information (including the mathematical explanation) is available at:
"Spin Stabilized Magnetic Levitation" (Martin D. Simon)
http://www.physics.ucla.edu/marty/levitron/
"A Toy Story  The Chemical Relevance of Earnshaw's Theorem, and How the Levitron® Circumvents It" (J. M. McBride)
http://www.chem.yale.edu/~chem125/levitron/levitron.html

Re: Levitating Magnets: Newsletter Challenge (12/12/06)