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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Earnshaw’s theorem applies to classical inverse-square law forces electric and fileytpe and also to the magnetic forces of permanent magnetsif the magnets are hard the magnets do not vary in strength with external fields.

Earnshaw’s theorem – Wikipedia

Limiting movement in that direction allows levitation with fewer than the full 3 dimensions available for movement note that the theorem is proven for 3 dimensions, not 1D or 2D. Potential safety concerns for each of the maglev system functional areas filehype identified.

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.

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

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. Though most of the force created by the images is repulsive, there is still the electromagnetic drag force created by the remaining currents in the passed loops, which can be thought of as coming from the previous images.

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. The German safety requirements were reviewed in terms of safety related functional areas of the following areas of the following seven maglev system elements: The frequency of the AC current is coordinated such that the field always repels the magnets in the object, sending it forward.


Earnshaw’s theorem was originally formulated for electrostatics point charges to show that there is no stable configuration of a collection of point charges. There are, however, several exceptions filerype the rule’s assumptions, which allow magnetic levitation.

Earnshaw’s theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic levitatikn of the charges.

Earnshaw’s theorem

However, I took a slight deviation to begin my studies with a simpler equation to model, the equation for the magnetic force between two plates of some finite area, given by:. Vehicle Rules and Safety. This report presents the results of a systematic review of the safety requirements selected for the Ifletype 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.

This works because the theorem shows only that there is some direction in leviration there will be an instability. I am unsure whether this drawback just applies to my Student version of Mathematica, or if my personal computer is to blame.

The safety of various magnetically levitated maglev trains underdevelopment for possible: 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. While a more general proof may be possible, three specific fileyype are considered here.

The current running through the electromagnets is constantly adjusted to maintain a steady distance between the train and the track. Here is a link to the Mathematica code used to produce the various graphs and plots in my project:.

This is why the EMS method is typically considered unstable; it requires a feedback control to vary the current passing through the electromagnet, to continuously adjust the magnetic field so that the object maintains a constant height above the track.

This means that the force field lines around the particle’s equilibrium position should all point inwards, towards that position. An example of this is the famous levitating frog see diamagnetism. 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.


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.

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:. However, I took a slight deviation to begin my studies with a simpler equation to model, the equation for the magnetic force between two plates of some finite area, given by: Then, propulsion is attained by the same methods as in the EMS system.

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

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 space. To extend upon this project, I would like to do several things: For my project, I will model the magnetic field produced by the superconducting magnet on the train, as well as the field produced by the tracks, and potentially, a combination of how the two fields interact. Refer to the Help section for more detailed instructions.

However, as the speed of the train fileype, the lifting force should increase proportionally, as the magnetic repulsion force increases. The Meissner effect and magnetic flux trapping are further explained and filetyype in the following videos: The dipole will only be stably levitated at points where the energy has a minimum.