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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The safety of various magnetically levitated maglev trains underdevelopment for possible implementation in the United States is ofdirect concern to the Federal Railroad Administration FRA. I am expecting my plots to show a strong relationship between force and distance from the track, such that the distance steadies out to a constant height over a length of time.

For this reason, some items on this page will be unavailable. Finally, the magnetic dipole of a ferromagnetic material a permanent magnet that is aligned parallel or antiparallel to a magnetic field will be given by. If I were able to compare these results with those for a rectangular coil of wire — a configuration more appropriate to maglev trains — I would expect the same patterns to appear, though the lifting force might take longer to approach the limiting value of the ideal image force, since the rectangular coil situation represents a real case rather than an ideal case.

Meanwhile, in an EDS system, no feedback control is necessary because, as the distance between the train and the track decreases, the magnetic force exerted on the train by the track increases, and vice-versa, until the train remains at a stable height above the track.

The goal of my project is to develop graphs for the magnetic fields produced by the object and the track, and, as I mentioned before, I would like to model the interaction of these fields as well. The Meissner effect and magnetic flux trapping are further explained and demonstrated in the following videos: Office of Research and Development. Potential safety concerns for each of the maglev system functional areas were identified.

There are, however, no known configurations of permanent magnets that stably levitate so there may be other reasons not discussed here why it is not possible to maintain permanent magnets in orientations antiparallel to magnetic fields at least not without rotation—see Levitron. These can thus seem to be exceptions, though in fact they exploit the constraints of the theorem.

Lastly, I think it would be most valuable to conduct experiments on my own, testing the relationships proposed by physicists in the past, and searching to develop a model to describe the exact relationship between the speed of the train or some scale model and fietype levitation force, magnetic drag force, and aerodynamic drag force that result.

See Maxwell’s equations for a more detailed discussion of these properties of magnetic fields. In paramagnetic and diamagnetic materials the dipoles are aligned parallel and antiparallel to the field lines, respectively. However, these eddy currents flow in a direction such that a magnetic field is produced that opposes the change in magnetic field entering the conducting track.

The safety of various magnetically levitated maglev trains underdevelopment for possible: 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:.

However, Gauss’s law says that the divergence of any possible electric force field is zero in free space. Views Read Edit View history. This report, one in a series of planned reports on maglev safety, Earnshaw’s theorem was originally formulated for electrostatics point charges to show that there is no stable configuration of a collection of point charges.

## Earnshaw’s theorem

In this case the Laplacian of the energy is always zero. Intuitively, though, it’s plausible that if the theorem holds for a single point charge then it would also hold for two opposite point charges connected together.

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Back to Previous Page. So, after having done extensive research into the various types ffiletype maglev technologies, I have found that the methods of electromagnetic suspension EMS and electrodynamic suspension EDS are the most developed and practiced types of magnetic levitation. If all of the surrounding field lines point towards the equilibrium point, then the divergence of the field at that point must be negative i.

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### joandrade | Modeling and Experimental Tools with Prof. Magnes

The induction process of the EDS system is depicted in the diagram below: To extend upon this project, Leitation would like to do several things: This report is the second in a series of levitatioh addressing the safety of high-speed maglev trains and presents the results of the review to determine the suitability ofGerman safety requirements for application to maglev systems as proposed for U. Bureau of Transportation Statistics.

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