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