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Conductors can have a relative permeability to alternating magnetic fields of below one, so some configurations using simple AC driven electromagnets are self stable.ĭynamic stability occurs when the levitation system is able to damp out any vibration-like motion that may occur.
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However, several possibilities exist to make levitation viable, for example, the use of electronic stabilization or diamagnetic materials (since relative magnetic permeability is less than one ) it can be shown that diamagnetic materials are stable along at least one axis, and can be stable along all axes. The forces acting on any paramagnetic object in any combinations of gravitational, electrostatic, and magnetostatic fields will make the object's position, at best, unstable along at least one axis, and it can be in unstable equilibrium along all axes. Static stability means that any small displacement away from a stable equilibrium causes a net force to push it back to the equilibrium point.Įarnshaw's theorem proved conclusively that it is not possible to levitate stably using only static, macroscopic, paramagnetic fields. In some cases the lifting force is provided by magnetic levitation, but stability is provided by a mechanical support bearing little load. However, servomechanisms, the use of diamagnetic materials, superconduction, or systems involving eddy currents allow stability to be achieved. įor example, the simplest example of lift with two simple dipole magnets repelling is highly unstable, since the top magnet can slide sideways, or flip over, and it turns out that no configuration of magnets can produce stability. Stability Įarnshaw's theorem proves that using only paramagnetic materials (such as ferromagnetic iron) it is impossible for a static system to stably levitate against gravity. P mag = B 2 2 μ 0 = 4π ×10 −7 N♺ −2 is the permeability of the vacuum. To calculate the amount of lift, a magnetic pressure can be defined.įor example, the magnetic pressure of a magnetic field on a superconductor can be calculated by: Įssentially all types of magnets have been used to generate lift for magnetic levitation permanent magnets, electromagnets, ferromagnetism, diamagnetism, superconducting magnets and magnetism due to induced currents in conductors.
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For example, the simplest example of lift would be a simple dipole magnet positioned in the magnetic fields of another dipole magnet, oriented with like poles facing each other, so that the force between magnets repels the two magnets. Magnetic materials and systems are able to attract or repel each other with a force dependent on the magnetic field and the area of the magnets. A superconductor levitating a permanent magnet
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