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Does the Levitron really defy Earnshaw's Law?
Posted on Monday, December 04, 2006 @ 20:52:48 GMT by vlad

Science FDT writes: Earnshaw's law of 1839 is based on Gauss's law. The principle behind Earnshaw's law is that no combination of inverse square law forces can provide a stability node for static levitation.

Atomic stability involving the balance between electrostatic repulsion and electrostatic attraction was once thought to disobey Earnshaw's law. The riddle has never been officially resolved, but anybody who has studied the graph that illustrates the inter atomic bonding force, and who has seen the stability node, knows that the repulsive force is not an inverse square law force. It drops off at a faster rate than the mutually attractive long range force. This faster drop off rate can be explained by centrifugal repulsion. See "Gravity Reversal and Atomic Bonding" at,

http://www.wbabin.net/science/tombe6.pdf

Experiments to measure the inverse square law relationship in the electrostatic repulsion of charged pith balls take their measurements from the equilibrium node where gravity and electrostatics cancel out. However, if such an equilibrium node exists, then the inverse square law relationship of the electrostatic repulsion has been disproved from the outset. It's little wonder that a correction factor has to be introduced in order to make the results fit the inverse square law relationship. It clearly isn't an inverse square law relationship.

Diamagnetic levitation is said to occur because diamagnetism is an induced effect rather than a permanent effect and that it is proportional to the magnetic field intensity from the source permanent magnet. Under standard theory, this should mean that diamagnetism has got an inverse square law dependence and hence no levitation should be possible. Clearly diamagnetism doesn't have an inverse square law dependence. See "Archimedes' Principle in the Electric Sea" at,

http://www.wbabin.net/science/tombe11.pdf

The levitron is a permanent magnet that levitates. It spins to give it gyroscopic stability in order to prevent it from turning over. It is said that this spinning motion means that the levitron is not static, and it is hence allowed to break Earnshaw's law. However the spinning motion has got absolutely no bearing whatsoever on the repulsive magnetic force which is pushing the levitron upwards. Clearly an equilibrium node has been reached with the downward force of gravity. The conclusion can only be that the magnetic force of repulsion is not obeying an inverse square law.

All the repulsive forces mentioned in this article can be explained by centrifugal force. There is no breakdown of Earnshaw's law. Earnshaw's law by its very nature, and by its roots in Gauss's law cannot be broken. The only conclusion that can ever be inferred from a situation that appears to defy Earnshaw's law, is that one of the balancing forces is not an inverse square law force.

Yours sincerely, David Tombe


 
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"Does the Levitron really defy Earnshaw's Law?" | Login/Create an Account | 2 comments | Search Discussion
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Magnetic Levitation and Earnshaw's Theorem (Score: 1)
by FDT on Wednesday, April 18, 2007 @ 03:01:01 GMT
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It has been suggested that Earnshaw’s Theorem is not breached in cases of magnetic levitation on the grounds that the magnetic force does not obey an inverse square law of distance.

An even more fundamental consideration has however been overlooked which might confirm both of these facts individually but undermine the argument that the fact of magnetic levitation actually proves the fact that magnetic force cannot be an inverse square law force.

We need to study the subject of coordinate frame origins in relation to forces that bear an inverse square law dependence on distance.

The solution for the B in Maxwell’s equations is B = μvXE. See section VII in 'The Unification of Electricity and Magnetism' at,

http://www.wbabin.net/science/tombe3.pdf [www.wbabin.net]

The inverse square law inherent in the Biot-Savart law is by virtue of the Coulomb force solution to the E vector in the solution to B, and based on the inverse square law of the Coulomb force, it is traditionally assumed that the inverse square law can be extrapolated throughout electromagnetic forces generally.

We are overlooking two very important factors. The first of these factors concerns the origin of the coordinate frame of reference. Traditionally we link the origin of the coordinate frame in the Biot-Savart law to the electric circuit that generates the magnetic field. However, we cannot do this in the case of a B vector deep in space that is linked to electromagnetic radiation. In such a case we are left with no choice but to centre the coordinate frame on an individual rotating electron positron vortex. It would further follow that perhaps we ought to be doing this in every situation and that the inverse square law in electromagnetism is something that only occurs on the microscopic scale. We have got absolutely no basis whatsoever to assume that the inverse square law continues to hold on the large scale when we sum over the entire sea of electron positron vortices.

The second factor that we are overlooking is the fact that the Biot-Savart law only contains the Coulomb force solution to E. It omits both the Lorentz force solution and the centrifugal force solution, which would destroy the overall inverse square law character of B. The Lorentz force solution is essential for electromagnetic induction and the centrifugal force solution is essential in ferromagnetic and electromagnetic repulsion as well as in diamagnetism and paramagnetism.

It seems therefore that based on coordinate frame origin considerations, we have got good reason to doubt the general validity of the inverse square law in large scale electromagnetism.

We can now further carry the argument about coordinate frame origins to Earnshaw’s Theorem itself. Originally Earnshaw’s Theorem was applied to arrays of static particles. The implication in such a scenario is that all distance dependent forces would be using exactly the same coordinate frame origins. There is no basis whatsoever to assume that Earnshaw’s Theorem applies in situations were two inverse square law forces are centred on different coordinate frame origins.

Magnetic levitation happens. It occurs when we place ring magnets, like pole to like pole, over a wooden stick. It happens in the Levitron.

If the magnetic force of repulsion should by any chance happen to be an inverse square law force, then its coordinate frame origin will be somewhere near the base of the apparatus. In the case of the gravitational force of attraction however, the coordinate frame origin is at the centre of the Earth. If the numerator of the magnetic force is less than the numerator of the gravitational force, then the different origins for the two graphs will mean that they can intersect and create a stability node. In other words, magnetic levitation by no means contradicts Earnshaw’s Theorem.

Yours sincerely, David Tombe



 

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