Could you create a magnet in shape of a hollow torus and magnetize it so that the interior is south and the exterior is north in order for it to act as a monopole? Is that possible? Thanks


No, you can't :)

There are no monopoles, I mean, if Maxwell's Euqations are correct, which is the state of knowlegde.

They say, that... well here are some formulations for equivalent statements:

  • the divergence of B is zero
  • microscopically there are no monopoles
  • the magnetic field lines are always closed loops

The picture of field lines has some problems [1], but is most vivid, and will suffice now. In your proposed monopole (the shape is irrelevant, by the way, why a torus?), all field lines go into the torus, but where should they go then, if they are not allowed to stop?!

Of course you can take a lot of bar magnets and glue them together to any hollow shape. But "the south pole" will not stay inside, all the field lines which went in have to go out somewhere, and will "annihilate" with the incoming [2].

[1] - with field lines, you do not see what happens when you have a superposition of two fields and the lines of the original fields cross... you have to think of them as a sum of vectors then.

[2] - Not neccessaryly in every point, but averaged. If the shape is a sphere, there will be no field at all, with a torus... there will be so quadrupole field left, I guess.

  • $\begingroup$ I learned in a theoretical math class that the torus acts in an infinite manner. They are not a closed loop like a sphere is which is why I ask. Would the energy would continue to circulate infinitely on the inside? $\endgroup$ – Dave Mar 21 '16 at 6:43
  • $\begingroup$ The magnetic field would just continue to circulate around the Taurus in an infinite loop I would imagine. $\endgroup$ – Dave Mar 21 '16 at 6:55
  • $\begingroup$ It's not about energy, the laws are stricter and apply to the magnetic field as written above. What you learned is probably, that the surface of a torus is equivalent to a plane in some sense. This is not connected to the notions of inside and outside from this boundary in space. $\endgroup$ – Ilja Mar 21 '16 at 6:55
  • $\begingroup$ In a sphere the magnetism gets halted and canceled out in the center in a Torus there is no center it's an infinite loop. $\endgroup$ – Dave Mar 21 '16 at 6:58
  • $\begingroup$ Well, luckily, physicist are not left alone with their imagination (which differs between persons) :) and even if Einstein sais, that goodreads.com/quotes/… then this applies to new research, not things that are known well. There, imagination plays us trick some times. $\endgroup$ – Ilja Mar 21 '16 at 6:58

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