A theorem due to Earnshaw proves that it is not possible to achieve static levitation using any combination of fixed magnets and electric charges. Static levitation. The answer is no, and this fact is referred to as the Earnshaw’s theorem. We will prove this assuming $q \gt 0$, but the proof is similar for $q \lt. PDF | A classical electrodynamical results known as Earnshaw theorem forbids the stable static levitation in stationary fields. Even though, permanent magnets.

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Is this a stable configuration? In the practical sense, one would be a fool to take the Earnshaw therom seriously. So our conjecture that Earnshaw’s theorem is false cannot be correct. Notice that this is true regardless of the polarity of the applied field, because the induced “currents” i. March 7, at 8: Maglev trains are one application.

In diamagnetics, electrons adjust their trajectories to compensate the influence of the external magnetic field, and this results in an induced magnetic field that points in the opposite direction to the external magnetic field.

### A proof of Earnshaw’s theorem – Diego Assencio

At a more practical level, it can be said that the Pauli exclusion principle and the existence of discrete electron orbitals are responsible for making bulk matter rigid.

Thompson, who tried to create mechanistic models of the atom involving tiny balls of charge in the late s and early s.

As a result, although each small domain is perfectly magnetized, the domains in an ordinary piece of iron are not aligned, so it has no significant net magnetic field. When we move the warnshaw magnet from the center, its magnetic field will be weaker in the diamagnets it moves away from and stronger in the diamagnets it moves towards.

Clearly, if the test charge is pushed directly towards one of the corner charges, it will be pushed back towards the center. The proof of Earnshaw’s theorem is very simple if you understand some basic vector calculus.

Since we observe stable levitation not to mention stable atoms and stable electronsit follows from Earnshaw’s theorem that there must be something else going on, viz. This is due to the phenomena called paramagnetism. It is interesting to note that Earnshaw himself was concerned with quite a different problem: In order for the exchange interaction to operate, the inter-electron distances must be just right, warnshaw these distances are obviously affected by the temperature, so there is a certain temperature, called the Curie temperature, above which theore, breaks down.

While your explanations of magnetic phenomena are insightful in themselves, they are not useful in concluding why the trolls are in error.

## Earnshaw’s theorem

About AD the Chinese began to use lodestone as a compass for finding directions on land, and soon afterwards Muslim sailors were using compasses to navigate at sea. In order to have stability, there must be a restorative force counter-acting any displacement away from the equilibrium point.

The blog covers topics in physics and optics, the history of science, classic pulp fantasy and horror fiction, and the surprising intersections between these areas. Thus, whether or not an atom has a net dipole field depends on the structure of the electron shells surrounding the nucleus. Further, because the energy for a dipole of fixed magnitude aligned with the external field will be the square root of the energy above, the same analysis applies.

Simultaneously, the forces produced by charges 1 and 3 begin to point in the same direction and reinforce one another.

These questions eventually pointed the way to quantum mechanical explanations of the structure of the atom, where the existence of stationary non-radiative states in which the electron has a nonzero momentum and therefore is not actually static resolves the above conundrum at a fundamental level. April 28, at 5: Europeans began using magnetic compasses for navigation around AD, probably bringing earnnshaw idea back from the Crusades.

## Is Magnetic Levitation Possible?

If the materials are not hard, Braunbeck ‘s extension shows that materials with relative magnetic permeability greater than one paramagnetism are further destabilising, but materials with a permeability less than one diamagnetic materials permit stable configurations. In modern terms, the theory may be stated roughly as:.

InSamuel Earnshaw proved what is now called Earnshaw’s Theorem, which states that there is no stable and static configuration of levitating permanent magnets. Finally, because both the divergence and the curl of a magnetic field are zero in the absence of current or a changing electric fieldthe Laplacians of the individual components of a magnetic field are zero. May 26, at 9: From Wikipedia, the free encyclopedia.

That being said, Maxwell is certainly one of the biggest influences on 20th century physics, and beyond! A superconductor is, in many respects, like a quantum-mechanical atom, but on a macroscopic scale, and it can support very large currents.