To: ruden@ug1.plk.af.mil (Edward Ruden)
From: ak@bethune.com (NEWS Alexandre Kampouris)
Newsgroups: sci.physics.electromag
Subject: Re: Proof of instability of magnetic levitation needed
Date: Tue, 1 Aug 1995 23:04:51
Cc: ak@bethune.com


>Cand someone please send me or refer me to a general proof that 
>*static* magnetic leviation by  *permanent* magnets is always unstable?
>I already know that if you use a superconductor, or keep parts moving
>that it can be done. e-mail responses appreciated.


Howdy!

In the book

"Electromagnetic Levitation and Suspension Systems",
B.V. Jayawant,
Publishers: Edward Arnold, London, 1981,

I quote the following passage from page 11:

...
The difficulties of achieving stable suspension or levitation are, however, 
highlited by an examination of the nature of the forces in the case when an 
inverse square law relates force and distance. Earnshaw [2] in his paper, 
which is now considered a classic by all workers in field of electromagnetic 
suspension, shows mathematically that it is impossible for a pole placed in a 
static field of force to have a position of stable equilibrium when a inverse 
square law operates; this fundamental calculation is known as Earnshaw's 
theorem. Braunbeck [3] carried out a similar analysis specifically for 
unvarying magnetic and electric fields, and deduced that suspension or 
levitation is possible when materials of mu_r<1 or epsilon_r<1 are introduced.

Suspension has been achieved using diamagnetic materials, and as a result of 
the effect of currents in the suspended objects.

[...]

It follows from Earnshaw's theorem and Braunbeck's analysis that stable 
suspension or  levitation is impossible with a system of permanent magnets (or 
fixed current electromagnets) unless part of the system contains either 
diamagnetic material (mu_r<1) or a superconductor (mu_r=0), and that it is 
altogether impossible to achieve levitation in electrostatic fields since 
there are no known materials with epsilon_r<1.

...


[2] Earnswaw, W., On the nature of the molecular forces which regulate the 
consitution of the luminferous ether., Trans. Camb. Phil. Soc., 7, pp 97-112 
(1842)

[3] Braunbeck, W. Free suspension of bodies in electric and magnetic fields, 
Zeitschrift für Physik, 112, 11, pp753-763 (1939)

I hope this helps. The references shouldn't be too hard to locate in a good 
university library.

Alexandre Kampouris
G&A Télécom S.A.R.F.
Montréal