Magnetism - stability of a ring with a sphere inside it?

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Discussion Overview

The discussion centers on the feasibility of a cylindrical ring made of permanent magnets containing a magnetic sphere that remains suspended without touching the ring's inner sides or falling through. The inquiry explores the principles of magnetic levitation and the conditions necessary for stability.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the possibility of static magnetic levitation, suggesting that the sphere would likely fall through or touch the sides of the ring.
  • Another participant outlines several necessary conditions for magnetic levitation, including the use of active electromagnets, contact points, rotation, superconductors, or specific materials like lightweight diamagnetic substances.
  • A later reply references Earnshaw's theorem, which posits that static, stable, free levitation of matter is impossible under certain force laws, unless diamagnetic materials are involved.
  • The extension of Earnshaw's theorem by Braunbeck is mentioned, indicating that static, stable, and free levitation requires at least one diamagnetic system present in the setup.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of the proposed setup, with some asserting that stable levitation is impossible under static conditions, while others provide theoretical frameworks that support this position. The discussion remains unresolved regarding the potential for alternative configurations or materials that might enable stability.

Contextual Notes

The discussion highlights limitations related to assumptions about the nature of magnetic forces and the specific configurations required for levitation, as well as the dependence on the properties of materials involved.

gazorpazorp
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Hey, is it possible to have a cylindrical ring (made of permanent magnet) and a magnetic sphere sitting inside it and staying in one place without touching the inner sides of the ring and not falling through?

The object doesn't necessarily have to be a sphere. If it would work with any other shaped object it would also be fine. The main problem is, would be able to stay inside.

The illustration:
http://imgur.com/a/woyvi
 
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I don't think so. Magnetic levitation via static fields is not stable and the object would most likely either fall through or touch the side.
 
Magnetic levitation will need one of those elements:
- active electromagnets controlling the position
- some point of contact of the levitated object (so it is not completely free)
- rotation of something, typically the levitated object
- superconductors
- strong permanent magnets and very exotic lightweight diamagnetic materials that can't carry any additional load
- strong electromagnets and diamagnetic materials
 
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Hello gazorpazorp,

mfb is right. There exists a theorem named after Earnshaw, which states that

static, stable, free levitation of matter is impossible, if the exerted forces show a 1/r^2 law

[S. Earnshaw: 1842 On the Nature of the Molecular Forces which regulate the Constitution of the Luminiferous Ether; Transactions of the Cambridge Philosophical Society 7, p. 97–112].

This theorem has been extended by Braunbeck to various kinds of electromagnetic levitation [Werner Braunbeck: 1939 Freischwebende K ̈orper I am elektrischen und magnetischen Feld; Zeit- schrift fu ̈r Physik 112 , p. 753]. He ends up with the conclusion:

Static, stable and free levitation of a system 1 in an electric, magnetic and gravitational field of a system 2 is impossible, unless diamagnetic matter is present at least in one of both systems.
 
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