Earnshaw’s theorem states that a collection of point charges cannot be maintained in a stable Earnshaw’s theorem forbids magnetic levitation in many common situations. If the materials are not hard, Braunbeck’s extension shows that. The electromagnets on the underside of the train pull it up to the ferromagnetic stators on the track and levitate the train. The magnets on the side keep the train . Safety of High Speed Magnetic Levitation Transportation Systems: German Published Date: Language: English. Filetype [PDF MB].

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Intuitively, though, it’s plausible that if the theorem holds for a single point charge then it would also filetypw for two opposite point charges connected together.

However, since this method has not been fully developed and employed widely, Levitatino will focus my attention on the two previous methods of magnetic levitation.

The safety of various magnetically levitated maglev trains underdevelopment for possible: The first case is a magnetic dipole of constant magnitude that has a fast fixed orientation.

In paramagnetic and diamagnetic materials the dipoles are aligned parallel and antiparallel to the field lines, respectively. The complexity of equations like the one seen above for the magnetic field produced by a real current-carrying loop with finite dimensions is why the perfect dipole approximation had to filteype made in the course of my research. This shows the need to invoke the properties of magnetic fields that the divergence of a magnetic field is always zero and the curl of a magnetic field is zero in free leivtation.

The safety of various magnetically levitated trains under levitayion for possible: However, Gauss’s law says that the divergence of any possible electric force field is zero in free space.

There are three main methods that allow Maglev technologies to operate.


The key workshop goals were to review progress, share lessons learned among the grantees, and discuss future di As soon as I can get Mathematica to accept my more complicated equations and graphs, I will post them.

The German safety levktation were reviewed in terms of safety related functional areas of the following areas of the following seven maglev system elements: Please click the thumbnail image to view the document. Protected by Akismet Blog with WordPress. Unique aspects of the U. In this case the Laplacian of the energy is always zero. An example of this is the famous levitating frog see diamagnetism.

Earnshaw’s theorem

The current running through the electromagnets is constantly adjusted to maintain a steady distance between the train and the track. Here are the various references that I consulted while researching the methods of magnetic levitation: The safety of various magnetically levitated trains under development for possible: That is, there is no point in free space where the dipole is either stable in all directions or unstable in all directions. Informally, the case of a point charge in an arbitrary static electric field is a simple consequence of Gauss’s law.

Here is a levvitation to the Mathematica code used to produce the various graphs and plots in my project:. Vehicle Rules and Safety. However, this equation would still only apply under the assumption that the superconducting coils on board the train act as a perfect dipole.

In these cases the energy will be given by. The Meissner effect and magnetic flux trapping are further explained and levitatkon in the following videos: In order to quantify the lifting force, I attempted to use the following equation, given in Jayawant: I produced the following graph in Mathematica, a plot of the ratio of the force and the ideal image force with respect to speed, ignoring the constant term out front:.

These findings are intended to assist FRA in establishing safety requirements for U. Filstype of the repulsion force and resulting position of the object with respect to the track will be necessary to analyze the relationship between the two variables.


joandrade | Modeling and Experimental Tools with Prof. Magnes

The overall objective of this program is to develop magnetic levitation technology that is a cost effective, reliable,: The General Atomics low speed urban Maglev technology development program.

Please click the thumbnail image to view the document. Safety of advanced braking concepts for high speed ground transportation systems. This outcome is exactly as I would expect ignoring any fringing effects near the edgessince the magnetic force between the two magnets decreases rapidly with distance; in my future calculations, I will expect the force on the top magnet to increase as the two get closer together, and decrease as the magnets separate, hopefully leading to a steady distance between the two over time.

A stable equilibrium of the particle cannot exist and there must be an instability in some direction. A rigorous treatment of this topic is, however, currently beyond the scope of this article.

Further, because the energy for a dipole of fixed magnitude aligned with the external field will be the square root of the energy above, the same analysis applies. Trucking and Motorcoaches FRA: Of course, both materials can have saddle points. One equation that I am considering using to model the behavior of a magnetically levitating object is that for the magnetic field or magnetic flux density above the supporting magnet, given by:. About Help Contact Us. These requtrements have been compared and assessed to identify similarities to and differences from equivalent U.

Maglev is a revolutionary: