Development of a way to overcome  the Earnshaw's theorem in the event  of magnetic levitation

Abstract

The paper is devoted to consideration of Earnshaw's theorem and to search the way how this theorem could be overcame. Earnshaw's theorem is one of the main theorems in electrostatics. It can be proven that by use of only ferromagnets it is impossible to hold the object in a gravitational field steadily. This statement is direct consequence of Earnshaw's theorem. But with the help of neodymium magnets, superconductors, and systems with vortex currents it is possible to achieve a stable levitation of the object during its movement. In current state neodymium magnets are considered to be the most powerful of all known permanent magnets. The problem with overcoming of unstable equilibrium in the movement of a levitating magnet still remains the most urgent problem of magnetic levitation in transport. The author of the paper proposes new device called "Levitron" which allows to prove that it is possible to achieve a stable equilibrium, and when moving the magnet – to achieve the transverse stabilization of the object. Stabilization with the phenomenon of magnetic levitation during movement can be achieved by use of the wings with different shapes, which are attached to the magnet. The wings make it possible to prevent the rotation of the magnet and stabilize its own motion in a horizontal plane. The device "Levitron" consists of two magnets: a permanent neodymium magnet and an electromagnet. The electromagnet (coil) is connected to the Hall sensor (which reduces the current in the coil while approaching to magnetic fiel). Thereby the distance from the flying magnet to the coil is adjusted. In the article two different types of wings are considered: a wing having a plate shape, and a wing that consists of two mutually perpendicular plates. As a result of the experiment, it was established that the maximum amplitude of the rotational vibrations of one-plane wing decreases to the half turnover, and for the wing of the cross-section form - to a quarter turnover. In modern transport, which uses magnetic levitation, a monorail is used which is a guide-rail. At high speeds, large friction forces occur, that limits the speed of the vehicle, and secondly, use a lot of energy that goes to overcome the friction force. In the case if the magnet movement will be balanced (that means that it’s rotating is completely removed) then monorail will not be needed at all. But it will lead to another problem: the effect of a magnetic field could have non-desirable influence to a person inside the vehicle. To solve this problem, we propose to use the "Faraday Cage", which is considered as a direction forto further research. Ref. 4, Fig. 3

Keywords

References

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Copyright (c) 2019 Дмитро Юрійович Свердліченко (Автор)