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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As it turns out, the equations for magnetic fields and forces that I was hoping to plot in Mathematica levittation too complicated for Mathematica to handle. Bureau of Transportation Statistics.

## Earnshaw’s theorem

This report is the second in a series of reports addr This levitaton proven at the very end of this article as it is central to understanding the overall proof. See Maxwell’s equations for a more detailed discussion of these properties of magnetic fields. A stable equilibrium of the particle cannot exist and there must be an instability in some direction. I found that there are many variables that influence how a maglev system will function, and that different types of variables affect different types of magnetic levitation.

The apporach employed in th Retrieved from ” https: 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.

In general, the German effort appears to ensure the same high level of safety for maglev trains that is expected in the United States for similar ground transportation technologies.

However, Gauss’s law says that the divergence of any possible electric force field is zero in free space. 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 the levitation force, magnetic drag force, and aerodynamic drag force that result.

Ideally, then, I could derive an expression for the ideal height the height that maximizes of the maglev train at any given speed. Vehicle Rules and Safety. However, the main component of this system that changes over time is the current flowing through the electromagnet, which would be extremely difficult to study analytically, and so I will focus on the other main maglev method. This report presents the results of a systematic review of the safety requirements selected for the German Transrapid electromagnetic EMS type maglev system to determine their applicability and completeness with respect to the construction and operation of maglev systems in the United States.

Refer to the Help section for more detailed instructions. These requirements were developed by a: The General Atomics low speed urban Maglev technology development program.

As for the plot of the magnetic fields, I expect that they will interact such that the repulsive force acting on the object will allow the object to remain above the track at a reasonable distance. 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.

Thus, I followed an assumption suggested by Kraftmakherand replaced this equation for the lifting force on a rectangular coil with the simplified equation for the lifting force on a magnetic dipole, given by Reitz as:. 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.

As explained before, EMS involves the electromagnets on board the train being attracted to the metallic track from underneath. Earnshaw’s filetpe has even been proven for the general case of 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.

Advanced Search Small Search Button. In paramagnetic and diamagnetic materials the dipoles are aligned parallel and antiparallel to the field lines, respectively. Thus, I followed an assumption suggested by Kraftmakherand replaced this equation for the lifting force on a rectangular coil with the simplified equation for the lifting force on a magnetic dipole, given by Reitz as: From now on, I will focus on finding the relationships between the speed of the train or, rather, the superconducting coils inside of itthe distance between the train and the tracks, and the magnetic lifting force and drag force that allow the EDS system to function.

The induction process of the EDS system is depicted in the diagram below: Furthermore, I could consider the effects of the magnetic forces that guide the train along the tracks, and how this force affects the magnetic lift and drag forces on the train in that case. 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. Additionally, for this magnetic dipole approximation, the ratio of lifting force to drag force remains fairly linear and very steep.

This report, one in a series of planned reports on maglev safety, Views Read Edit View history. Protected by Akismet Blog with WordPress. The German safety requirements were reviewed in terms of safety related functional areas of the following areas of the following seven maglev system elements: This was first proven by British mathematician Samuel Earnshaw in The second method, called electrodynamic suspension EDSrequires that both the levitating object and the track exert a magnetic field, so that the object is levitated by the repulsive force between the two fields.

Here are the various references that I consulted while researching the methods of magnetic levitation:. Additional effects that allow maglev trains to remain at a steady height above the track include the Meissner effect, and magnetic flux trapping.

### Earnshaw’s theorem – Wikipedia

I may also look into magnetic pressure, and how this variable might explain how and why the object levitates. The first, electromagnetic suspension EMSinvolves electromagnets on the levitating object that are oriented toward the rail from below. The safety of various magnetically levitated trains under development for possible: Then, to propel the object forward, some additional method must be employed, whether it involves the use of a propeller, an engine, or propulsion coils, the latter of which is explained in the section below.

Diamagnetic materials are excepted because they exhibit only repulsion against the magnetic field, whereas the theorem requires materials that have both repulsion and attraction. This report presents the results of a systematic review of the safety requirements selected for the German Transrapid: