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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joandrade | Modeling and Experimental Tools with Prof. Magnes

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. The key workshop goals were to review progress, share lessons learned among the grantees, and discuss future di The dipole will only be stably levitated at points where the energy has a minimum.

The current running through the electromagnets is constantly adjusted to maintain a steady distance between the train and the track. However, since magnetic attraction varies inversely with the cube of distance, minor changes in the distance from the rail cause the lifting force to vary greatly.

Earnshaw’s theorem – Wikipedia

The safety of various magnetically levitated trains under development for possible: Refer to the Help section for more detailed instructions. Additional effects that allow maglev trains to remain at a steady height above the track include the Meissner effect, and magnetic flux trapping.

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: The safety of various magnetically levitated maglev trains underdevelopment for possible: The energy U of a magnetic dipole with a magnetic dipole moment M in an external magnetic field B is given by.

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. For a particle to be in a stable equilibrium, small perturbations “pushes” on the particle in any direction should not break the equilibrium; the particle should “fall back” to its previous position.


Then, to make the object move forward along the track, propulsion coils carrying AC current generate a continuously-changing magnetic field that exerts a force on the magnets in the object.

For more information about this message, please visit this page: Earnshaw’s theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. The challenge lies in transferring the experience of Germany to the U. One of the easiest ways to model the behavior of these types of maglev systems is by using the equation for magnetic pressure, given asfrom which we can derive the amount of force that the bottom of the train feels towards the track in a given area.

An example of this is the famous levitating frog see diamagnetism. This report, one in a series of planned reports on maglev safety, In order to quantify the lifting force, I attempted to use the following equation, given in Jayawant:. Additionally, I will lvitation the equation for the force of repulsion on the object by the supporting magnet, given by the equation:.

Here is a link to the Mathematica code used to produce the various graphs and plots in my project: 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 ifletype the track increases, and vice-versa, until the train remains at a stable height above the track. A rigorous treatment of this topic is, however, currently beyond the scope of this article.

As the top coil is pulled downwards by gravity, the two fields will interact much more, increasing the repulsion force, and thus levitating the train containing the superconducting coils.


Maglev trains are one application. Additionally, for this magnetic dipole approximation, the ratio of lifting force to drag force flletype fairly linear and very kevitation. Pseudo-levitation constrains the movement of the magnets usually using some form of a tether or wall.

A stable equilibrium of the particle cannot exist and there must be an instability filetpe some direction. 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.

Earnshaw’s theorem

Because the ratio of lifting force to drag force is one measure of the efficiency of a maglev system i. As explained before, EMS involves the electromagnets on board the train being attracted to the metallic track from underneath.

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:. Clearly, the force falls off extremely quickly with respect to distance, so I am expecting my other graphs to have a range of many fractions of a meter.

Select up to three search categories and corresponding keywords using the fields to the right. The frequency of the AC current is coordinated such that the field always repels the magnets in the object, sending it forward.

Please click the thumbnail image to view the document. The induced EMF in the lower loop, and the lagging induced current, are graphed with respect to time below. As a practical consequence, this theorem also states fletype 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.