April 29, 2020 0 Comments

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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It is not possible to make a bar magnet levitate in a stable position only through the use of other bar magnets. The field and particle trajectory simulator Industry standard charged particle optics software Refine your design: I would disagree that I proved his assumption right!

That is, paramagnetic materials can be unstable in all directions but not stable in all directions and diamagnetic materials can be stable in all directions but not unstable in all directions. Magnetism has been known since ancient times.

Earnshaw’s theorem

You could even do it with movable permanent magnets. It’s worth noting that this is due to the intrinsic spins of the individual electrons, not due to the orbital motions of the electrons as is the case with theorm and paramagnetism.

Create a free website or blog at WordPress. Sign up using Email and Password. This means that the earnshqw field lines around the particle’s equilibrium position should all point inwards, towards that position. Configurations of classical charged particles orbiting one another are unstable due to losses of energy by electromagnetic radiation.


In broad terms, diamagnetism and paramagnetism are different types of responses to an externally applied magnetic field.

Maybe I can put it more concisely: Intuitively, whether it is inverse unity, square, cube, or even higher power, the static field model will be unstable. It does NOT even apply to magnetic systems, since magnetism is a property of moving electric charges currents.

It is best to imagine the bar magnets standing up, i. Intuitively, though, it’s plausible that if the theorem holds for a single point charge then it would also hold for two opposite point charges connected thforem.

That being said, Maxwell is certainly one of the biggest influences on 20th century physics, and beyond!

Magnetic Levitation

You should also prove that harmonic functions cannot have all zero eigenvalues In accord with Lenz’s Law, these currents oppose any applied field, so it’s actually possible to achieve stable levitation of a permanent magnet over a superconductor.

Physics Stack Exchange works best with JavaScript enabled. Notice that this is true regardless of the polarity of theorme applied field, because the induced “currents” i. 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 earnsyaw therefore is not actually static resolves the above conundrum at a fundamental level.

The explanation for diamagnetism lies not in the spin of an electron but in the orbit of an tneorem around the nucleus of an atom, and this thekrem motion itself acts like a little current loop. The levitating magnet itself is supported between a pair of plates made of bismuth which — and this is in fact the key point — is a strongly diamagnetic material.


As soon as the field is removed, the atomic dipoles tend to slip back into random orientations. Each electron in an atom can be regarded as having some “orbital” motion about earnshae nucleus, and this moving charge represents an electric current, which sets up a magnetic field for the atom, as shown below.

Earnshaw’s theorem was originally formulated for electrostatics point charges to show that there is no stable configuration of a collection of point charges. There are, however, several exceptions to the rule’s assumptions, which allow magnetic levitation. However, in ferromagnetic substances, the intrinsic spins of many of the electrons are aligned, both within atoms and between atoms. Classically an electron would be expected to collapse onto a proton, assuming it had no angular momentum.

A theorem due to Earnshaw proves that it is not possible to achieve static levitation using any combination of fixed magnets and electric charges.

Levitation and diamagnetism, or: LEAVE EARNSHAW ALONE!!! | Skulls in the Stars

The above is easily corroberated by winding a pancake radiator which is the equivalent to a Gaussian field in equilibrium which, with the maximum density of wire surfacecorrelates with maximum residing static particles for the creation of loss less radiation. One example is the compound Fe 3 O 4also called lodestone, which the ancient Greeks found lying around in Magnesia. MT on Apr 06,