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[I believe that this question is very different than the question about arranging magnets into a sphere. Solenoids are ruled by Ampere's Law and magnets are not. Ampere's Law is what could make it work.]

I am wondering if Ampere's Law can be a loophole around Gauss's law of magnetism (Gauss's Law not allowing for magnetic monopoles). With solenoids arranged in a sphere, particularly if you had two of these solenoid-sphere's (one positive and one negative), couldn't the field lines be induced to extend out rather than loop back around on themselves?

Arrange solenoids into a sphere so that the outside of the sphere is made only of the positive ends of the solenoids, and the inside of the sphere only has the negative end of the solenoids (or vice-versa). Doesn't Ampere's Law suggest that there would be no place for the field lines to reconnect? The contour integrals have a maximum capacity that is used up by the field lines moving towards (or away from) the center. Could this not create a magnetic monopole?

Whether or not this would work, surely someone has done the experiment, right? I cannot find evidence of this experiment. I really want to know how this experiment turned out, does anyone know?

Erik Gecas
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If your solenoids were thin enough to behave approximately as Dirac strings, with an effective monopole at each end, your sphere would have an equal number of negative and positive magnetic charges. A Gaussian surface that enclosed the entire sphere would still have zero magnetic flux. Symmetry considerations might suggest you'd have a monopole-like magnetic field in the region between the negative and positive shells, as in the case for electric charges, but the presence of the many solenoids extending from the sphere of negative ends to the sphere of positive ends would make a physical implementation quite complicated --- nothing at all like the symmetric case for electric fields, where a "small" charge like a nanocoulomb is made of $10^{10}$ fundamental charges.

rob
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