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Banned on April 7, 2007 Registered Member #277
Joined: Fri Mar 03 2006, 10:15AM
Location: Florida
Posts: 157
The below quote is from located about halfway down the page.
"A diamagnetic object can levitate only close to an inflection point of the vertical component of the magnetic field,6 where d2BZ/dz2 = 0. Note that this is a purely geometrical condition, which does not depend on the field strength. The spatial extent of the region of stable levitation is typically a small fraction of the magnet’s size".
I don't claim to fully understand the above equation... my guess is that it means that the physical SIZE of a magnet (not just field strength) is crucial to how high a diamagnetic object can be levitated above Magnet "A". Or said another way, to achieve a higher levitation of a diamagnetic object, Magnet "A" must be replaced by magnet "B" which is physically larger? I appreciate someone clearing up my cloudy conception of the above. Thanks. CM
Registered Member #146
Joined: Sun Feb 12 2006, 04:21AM
Location: Austin Tx
Posts: 1055
I think id agree with your guess on that. Since the usable inflection point is only so large for a particular magnet size, you would be limited in the object size that could be levitated there.
But i too am having a hard time with this one. It seems relatively easy to make a constant B field (dB/dz = 0) with even some helmholtz coils, so it seems like it would be even easier to make d^2B/dz^2 = 0 (approximately). I must be missing something, otherwise it would be too easy, disagreeing with what he later says about how delicate the setup is.
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
They mean that the second derivative of the B field should be minimum at that point, and greater all around it, I think. The second derivative is something to do with magnetic energy, and the principle of least action says that systems always try to minimise their total energy, so what you have is a kind of little pocket in space of minimum magnetic energy that the item will settle into.
Registered Member #146
Joined: Sun Feb 12 2006, 04:21AM
Location: Austin Tx
Posts: 1055
So very similar to the principal of acoustical levitation, in a sense that the levitated object will settle into a low pressure zone (though these are caused by standing waves in a chamber).
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Equation interpretation please
