I have only learned high-school physics but would like to gain insight into how Earnshaw's Theorem makes stable bearings that use magnetic levitation from permanent magnets impossible or impractical.
Hence, or otherwise, what is meant by the following?
Passive magnetic bearings (PMB) achieve contact-free levitation of an object by permanent magnetic attractive or repulsive forces. Depending on the configuration, stabilization in radial, axial and tilt direction are possible. It is, however, not possible, to stabilized all degrees of freedom of a body by passive magnetic levitation, alone.
I'm particularly interested in the last sentence.
My aim is to find out if it possible to engineer such a bearing of a size which could fit in your hand and be rotated at greater speeds with less push exerted, than most good bearings.
Source of quote: http://www.magneticbearings.org/technology-2/technologies/passive-bearings/
Best Answer
A "static" magnetic field, like you get from a bar magnet, is unchanging. Earnshaw's theorem says that there is no configuration of these stationary magnets alone which can keep another magnet in one place.
If you have magnets which are rings, for example, you may notice that if you put them both on a pencil sticking through the middle, pointing up from a desk, in one of the ways you orient them, they stick together; in another way you orient them, one of them floats above the other one. But you may also notice that you cannot keep the one on top floating without the pencil in the middle to hold it in place. It will always find some way to twist around so that it can stick to the other magnet.
Earnshaw's theorem says that actually, no set of magnets will do this. If you use a stronger magnet to try to discourage twisting, then the stronger magnet will now induce some other direction which the object wants to twist around in order to attract to the new bigger magnets. You cannot win.
It also says the same thing even if you add electric charges to all of your magnets, too. There is always a direction that the object can move which will reduce its electrostatic potential energy, and when it does so, it will gain some kinetic energy moving in that direction, twisting it out of its normal configuration.
With that said, we can break the assumptions of the theorem by using things like superconductors or computers that dynamically change the fields. We just can't do it "passively."