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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Earnzhaw fields are used by researchers to trap ions for study in so-called quadrupole ion traps. It is also possible to buy gadgets that levitate objects in this way. April 15, at 9: The simple point is that magnetism follows inverse third power law, not inverse square.

This entry was posted in Physics. Only five elements have electron shell earnshqw that support ferromagnetism, namely, iron, earnshxw, nickel, gadolinium, and dysprosium. The static force as a function of position F x acting on any body in a vacuum due to gravitation, electrostatic, and magnetostatic fields will always be divergence free: 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 contour lines are in red. Notify me of new posts via email. Something like quantum mechanics and the exclusion principle is required.

We may consider these loops to be randomly oriented, as in the case of paramagnetism. You could even do it with movable permanent magnets. In these cases the energy will be given by.

Equilibrium is also not a problem, because there is obviously a configuration at the boundary between falling and rising. They act very much like a pair of fellows escorting a drunk friend home: This paramagnetic attraction effect is much stronger than the diamagnetic repulsion, so paramagnetism usually masks the effect of diamagnetism for such substances.

Edward Arnold, London, May 26, at 9: The magnetic property of lodestone Fe 3 O 4 was mentioned by the Greek philosopher Thales c.

## Is Magnetic Levitation Possible?

Posted on April 13, by skullsinthestars. It does NOT even apply to magnetic systems, since magnetism is a property of moving electric throrem currents.

These are all “transition elements”, with partially populated 3d inner electron shells.

Admittedly it may not have been clear in Earnshaw’s day that the book’s interaction with the desk was via electromagnetic forces, but Earnshaw’s theorem actually applies to any classical particle-based inverse-square force or combination of such forces. The energy U of the magnetic dipole M in the external magnetic field B is given by. There is no classical analogy.

### Magnetic Levitation

Brandt, Science, Jan exrnshaw Pseudo-levitation constrains the movement of the magnets usually using some form of a tether or wall. It is always annoying to me when someone flashes a bunch of mathematical mumbojumbo in our faces and says something is impossible. Earnshaw’s theorem forbids magnetic levitation in many common situations. Due to a finite resistance, the induced changes in electron trajectories disappear after a short time, but you can create a permanent screening current at the surface by applying an oscillating field, and conducting bodies behave just like superconducting bodies.

## Earnshaw’s theorem

So our conjecture that Earnshaw’s theorem is false cannot be correct. If we pretend we have a collection of bar magnets arranged in a square, another bar magnet placed in the center of the square will not be in a stable position, and will be pulled and twisted around out of the center, and likely towards one of the other magnets:.

Our would-be Earnshaw basher highlights an important issue that is always good to remember in theoretical physics: March 11, at 2: Hence there is a repulsive force between the magnet and the conducting ring. Technically any body sitting on a surface is levitated a microscopic distance above it.

Thus the integral of the force over any closed surface in empty space is zero, which implies that if it points inward on some parts of the surface, it must point outward on other parts, so it is clearly not a stable equilibrium point.

Maglev trains are one application. Email Required, but never shown.

### electrostatics – Proving Earnshaw’s theorem is subtle in three-dimensions! – Physics Stack Exchange

If we pretend we have a collection of bar magnets arranged in a square, another bar magnet placed in the center of the square will not be in a stable position, and will be pulled and twisted around out of the center, and likely towards one of the other magnets: The problem is stability.

From Wikipedia, the free encyclopedia. March 8, at 4: Geometrically, this follows from the mean value property of harmonic functions. This means that the force field lines around the particle’s equilibrium position should all point inwards, towards that position.