WardRichard E. Foster IIMonday, March 12, 2001Studies show that people are reluctant to abandon automobile use for trips of less than 100miles, while planes are most efficient at trips of over 500 or 600 miles. The trips in between thesedistances are those that will be best served by magnetic levitation (Maglev) transportationsystems. By replacing short, inefficient commuter flights between cities, maglev trains mighteventually link sections of the country, ease traffic congestion on the highways, and help alleviateovercrowding at airports. Aside from its transportation benefits, a maglev system will create jobsfor a wide range of industries.Magnetic levitation uses magnetic waves to suspend and propel vehicles along a guidewaysimilar to monorail guideways. To understand how this works we will go into a little physics. Atheorem devised by William Earnshaw proves that it is not possible to achieve static levitationusing any combination of fixed magnets and electric charges. Static levitation means stablesuspension of an object against gravity. There are however, a few ways to levitate by gettingaround the assumptions of the theorem.The proof of Earnshaws 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 magnostatic field will always be divergences. divF=0. At a point of equilibriumthe force is zero. If the equilibrium is stable the force must point in towards the point in towardsthe point of equilibrium on some small sphere around the point. However, Gauss theorem, theintegral of the radial component of the force over the surface must be equal to the integral of thedivergence of the force over the volume inside which is zero. This theorem even applies to extended bodies which may even be flexible and conducting solong as they are not diamagnetic. They will always be unstable to lateral rigid ...
