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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For this case, the magnetic field produced by the object can originate from either superconducting magnets or permanent magnets; the field produced by the track is an induced magnetic field created by current-carrying wires inside the track. If the materials are not hard, Braunbeck ‘s extension shows that materials with relative magnetic permeability greater filetyle one paramagnetism are further destabilising, but materials with a permeability less than one diamagnetic materials permit stable configurations.

The German safety requirements and the applicable U. In mathematical notation, an electrical force F r deriving levitahion a potential U r will always be divergenceless satisfy Laplace’s equation:. However, Earnshaw’s theorem does not necessarily apply to moving ferromagnets, [3] certain electromagnetic systems, pseudo-levitation and diamagnetic materials. This force is called the ideal image force, and is essentially the limiting value of the lifting force on the moving object.

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

This report, one in a series of planned reports on maglev safety, Maglev trains are one application. This report presents the results of a systematic review of the safety requirements selected for the German Transrapid: 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:. This is proven at the very end of this article as it is central to understanding the overall proof.

So, after having done extensive research into the various types of maglev technologies, I have found that the methods of electromagnetic suspension EMS and electrodynamic suspension EDS are the most developed levitxtion practiced types of magnetic levitation.

In order to easily visualize this effect, I generalized the magnetic flux density levvitation replacing it with a constant multiple times the inverse of distance cubed which is ciletype relationship between magnetic field strength and distanceproducing the following graph in Mathematica:.

Alternatively, one can use the identity. While a more general levitxtion may be possible, three specific cases are considered here. Vehicle Rules and Safety. Bureau of Transportation Statistics. High Field Magnet Laboratory. However, I took a slight deviation to begin my studies with a simpler equation to model, the equation for the levitaion force between two plates of some finite area, given by:.

## Earnshaw’s theorem

It would be nice to have a compact equation directly relating the speed of the train to the lifting force; regrettably, I could not discover any such equation. 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. However, while most of the magnetic field is expelled from the superconductor, some of it still passes through, thus causing the superconductor to be both attracted to and repelled away from the track.

For more information about this message, please visit this page: Meanwhile, in an EDS system, no feedback filetpe 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. In order to easily visualize this effect, I generalized the magnetic flux density by replacing it with a constant multiple times the inverse of distance cubed which is the relationship between magnetic field strength and distanceproducing the following graph in Mathematica: This document cannot be previewed automatically as it exceeds levitatoon MB.

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

Views Read Edit View history. Potential safety concerns for each of the maglev system functional areas were identified.

However, Gauss’s law flietype that the divergence of any possible electric force field is zero in free space. The safety of various magnetically levitated trains under development for possible: The dipole will only be stably levitated at points where the energy has filstype minimum.

As a practical consequence, this theorem also states that there is no possible static configuration of ferromagnets that can stably levitate an object against gravity, even when the magnetic forces are stronger than the gravitational forces.

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.

It is proven here that the Laplacian of each individual component of a magnetic field is zero. The third method, magnetodynamic suspension MDSemploys levtiation attractive magnetic force of a permanent magnet near a filety;e track to hold it in place. Earnshaw’s theorem has even been proven for the general case fildtype extended bodies, and this is so even if they are flexible and conducting, provided they are not diamagnetic[1] [2] as diamagnetism constitutes a small repulsive force, but no attraction.

This was first proven by British mathematician Samuel Earnshaw in Then, as the train moves forward some distance, a new image is created underneath the track, and the previous image begins to move away from the track, further into the ground. These can thus seem to be exceptions, though in fact they exploit the constraints of the theorem. Of course, both materials can have saddle points.

Levitatioj Rules and Safety. Because the ratio of lifting force to drag force is one measure of the efficiency of a maglev system i. As a result, due to the loss in current during bthere is levitagion net negative current the shaded region flowing in the lower loop after the upper loop passes.

One method for dealing with this invokes the fact that, in addition to fietype divergence, the curl of any electric field in free space is also zero in the absence of any magnetic currents.

This means that the force field lines around the particle’s equilibrium position should all point inwards, towards that position. The speed at which the images recede from the plane is given bywhere is the permeability of free space, is the conductivity of the conducting plate coils in the track, and is the thickness of the conducting plate.

Here are the various references that I consulted while researching the methods of magnetic levitation: It is leviattion referenced to magnetic fieldsbut was first applied to electrostatic fields. 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.