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Ring Magnet

  1. Sep 19, 2010 #1
    Has anyone heard of a permanent magnet in the shape of a ring or toroid with no poles? I believe that one could be made by winding a ring of magnetic material, such as steel, with a wire winding, like one winding of a toroidal transformer. DC current could then be passed through the winding for a sufficient length of time and then the winding removed. One would then have a magnet with no poles, the flux circulating around the ring. I believe that if the ring were uniform and symmetrical, there would be no magnetic field external to the ring. I cannot think of a practical use for such a magnet but just am interested in the principle. Comments?

  2. jcsd
  3. Sep 19, 2010 #2


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    Is this material a hollow torus or a solid?
  4. Sep 20, 2010 #3
    Remember those old horseshoe shape magnets with a soft iron "keeper" connecting the poles?
    There you have it.
    Note that there is still some external magnetism, however.
  5. Sep 20, 2010 #4

    I was thinking of solid, but I do not believe that it would make any difference.


    Yes, it is similar, but the maximum symmetry of the torus is necessary to eliminate any external field.

  6. Sep 20, 2010 #5
    Binside is everywhere parallel to the boundary between air and the magnetic material. If H-tangential is continuous across this boundary, then the tangential Bair = Binside/μ, where μ is the relative permeability.
    Would there be an Aharanov-Bohm effect


    on any charged particle going through the hole in the ring? Is there a practical use?

    Bob S
  7. Sep 20, 2010 #6
    Aharonov–Bohm effect:
    Schematic of double-slit experiment in which Aharonov–Bohm effect can be observed: electrons pass through two slits, interfering at an observation screen, with the interference pattern shifted when a magnetic field B is turned on in the cylindrical solenoid.

  8. Sep 20, 2010 #7
    As pointed out by Bob S, even toroidal symmetry will not eliminate the external field if you only have a permanent magnet.

    You could encase the torus in a superconductor to shield the magnetic field, and truly confine it.

    A tightly wound toroidal coil with DC current is a cheaper way to have field inside and essentially zero field outside.

    In other words, don't remove the windings from the ring, and don't turn off the current. Basically, the field from the current will cancel the field from the core, on the outside of the ring. (you can also think of this in terms of the boundary condition mentioned by Bob S, but now include the sheet linear current density K: i.e. Ht1-Ht2=K, which allows Ht2=0 on the outside)
    Last edited: Sep 20, 2010
  9. Sep 22, 2010 #8
    The lack of an external field is the result of symmetry, not the particular source of the field. The lack of poles implies no external field. If there were an external field, there would be poles. If there is an external field, what does it look like?

  10. Sep 22, 2010 #9
    If there are no surface currents (coils), Curl H is continuous across the boundary between air and the ring (magnetic material), meaning Curl H = 0, or tangential Hair = Hring.. So Bair = μ0Hair = Bring/μ, where μ is the relative permeability of the ring material at field Bring.

    Bob S
  11. Sep 22, 2010 #10
    Bob S,

    So what does the field look like? What is its shape?

  12. Sep 22, 2010 #11
    Now, that's an interesting proposal. But will the counter-currents in the superconductor, required for cancelation of external fields, also cancel all internal fields?
  13. Sep 22, 2010 #12
    http://unitednuclear.com/index.php?main_page=product_info&cPath=70_71&products_id=290 [Broken]
    Last edited by a moderator: May 4, 2017
  14. Sep 23, 2010 #13
    Most commercial ring magnets actually have the poles on the "flat" sides.
    The same is true for the above link, but harder to envision.
    Last edited by a moderator: May 4, 2017
  15. Sep 23, 2010 #14
    Well then I'm puzzled by the question - what defines a pole? Like what makes the north pole of a magnet a pole, and not the middle of it?
  16. Sep 23, 2010 #15
    That's an interesting question about an "interesting proposal". Keep in mind that the proposal is not my invention. I've just read discussions on the Aharonov–Bohm effect that talk about using superconductors to remove any doubt that the electron is traveling in a field free region.

    I'm not very knowledgable about superconductor theory so I hesitate to answer definitively. My best guess is that generally the internal fields won't cancel, and that the internal field will always be strengthened. But, I wouldn't be overly surprised if an expert comes here and tells us that it is possible to configure a superconducting shield with a particular core material in a way that cancels both internal and external fields. It seems counter-intuitive to me, but my intuition has failed me often enough that I'm not surprised when it happens.
  17. Sep 23, 2010 #16
    That's actually a good question. A magnetic "pole" is one of those things that everyone talks about and assumes is straightforward, until they try to define it. I like to think of a pole as the part of a magnet that has the most concentrated field that is typically coming mostly perpendicularly to the surface.

    For example, a typical bar magnet or a spherical magnet (like the earth) are like dipoles, and the dipole field pattern (you can look it up in any EM book) has clear poles. Magnetic field lines are always closed, so the north poles field lines circulate back to the south pole.

    The OPs example is interesting because there is no clearly identifiable pole, due to the symmetry. The field lines internal to the toroid just circulate back on themselves always. The external field lines also circulate back on themselves.

    However, typical ring magnets aren't magnetized in this way. They can be magnetized so that the top and bottom (think heads and tails of a coil-like object) are the north and south poles. Also, they can be magetized so that one side of the circular cross section is the north pole and the oposite side is the south pole. Think about a two dimensional version of the earth (circle rather than sphere) with a north and south pole.
    Last edited: Sep 23, 2010
  18. Sep 23, 2010 #17
  19. Sep 25, 2010 #18
    All magnetic field lines of a permanent magnet must pass through the magnetic material, since the iron atoms are the source of the field lines, and therefore the lines must pass through the iron atoms. Any external field lines must therefore pass through the surface of the torus. There is no way for this to happen without violating symmetry. Thus, there can be no external field.

  20. Sep 25, 2010 #19
    Uh... I don't think that's true. Field lines do not have to stay within a material, though a majority will.
    For example, take a horseshoe permanent magnet and bridge the north/south poles with a soft iron "keeper''
    According to your thoughts, then, there can be no external field.
    This is NOT the case.
    With that magnet and it's keeper, bring it close, BUT NOT TOUCHING a paper-clip.
    The paper-clip WILL be attracted.
    Just not as much, by far, if there were no "keeper"
  21. Sep 25, 2010 #20

    I did not say that the lines had to stay within the magnetic material; I said that they have to pass through the material. In other words, there cannot be any lines no part of which exist in the material.

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