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Beating Earnshaw's theorem

  1. Oct 23, 2009 #1

    I've been doing some research on an idea of mine, part of which involves levitating a sphere. Apparently Earnshaw's theorem makes this very difficult; but I'm having a hard time imagining why. I'm imagining the sphere as a magnet, with the north pole over the entire outer surface of the sphere and the south pole over the entire inner surface of the sphere. Two magnetic rings circle around the sphere, each parallel to the equator, but one above and one below the equator. These magnetic rings come close to contact with the sphere, but not quite. The rings are oriented so that their north pole is facing the sphere, causing a repulsive force between the rings and the sphere. The rings are held in place by a bar (or whatever) that is attached to both rings and the ground, keeping the rings firmly in place.

    With this setup, would the sphere not stably remain levitated within the rings? I'm trying to understand how Earnshaw's theorem would allow this setup to be unstable. Whichever way the sphere moves, it will move towards a repulsive magnet, which will cause it to move back to an equilibrium right in the middle of the rings. Right?
  2. jcsd
  3. Oct 23, 2009 #2


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    Science Advisor

    You could probably make a magnet like that by having hundreds of cone shaped magnets with the pointy ends magnetized as south poles and all pointing inwards. They would tend to repel each other, of course. Maybe you could glue them together.

    Until you got it to be a hemisphere, there would be a return path for the magnetic fields of most of these magnets.
    However, as you went beyond a hemisphere, the magnetic fields of the magnets could only return to the other end of the magnet by trying to demagnetise another magnet, so the two magnets would tend to cancel each other out.

    When you reached the stage of having a sphere, the net magnetic field outside the magnet would be close to zero.

    Nice try, but I don't think it is going to work.
  4. Oct 24, 2009 #3


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    Staff: Mentor

    As vk6kro points out, your sphere cannot be magnetized the way you want. Why not just use eddy current levitation? Or diamagnetic material levitation?


  5. Oct 24, 2009 #4
    Yes, I suppose eddy current or diamagnetic levitation would work. Which of these would require less energy? I would like to be able to levitate the sphere for a couple hours at a time at least with a load of a couple hundred pounds or so, using a battery. How big of a battery would I need to be able to do this?

    I know, the equations to figure all this out on my own are out there somewhere, but I really don't know much about this subject and it would be very helpful if someone could just give me a rough idea if what I'm trying to do is feasible at all. Thanks.
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