Is Magnetic Levitation Possible?
A theorem due to Earnshaw proves that it is not possible to achieve static levitation using any combination of fixed magnets and electric charges. Static levitation means stable suspension of an object against gravity. There are, however, a few ways to levitate by getting round the assumptions of the theorem. In case you are wondering, none of these can be used to generate anti-gravity or to fly a craft without wings or jets. Earnshaw’s Theorem The proof of Earnshaw’s theorem is very simple if you understand some basic vector calculus. The static force as a function of position F(x) acting on any body in vacuum due to gravitation, electrostatic and magnetostatic fields will always be divergenceless. divF = 0. At a point of equilibrium the force is zero. If the equilibrium is stable the force must point in towards the point of equilibrium on some small sphere around the point. However, by Gauss’ theorem, / / | F(x).dS = | divF dV /S /V the integral of the radial component of the force o
