### Question

If I carve out a perfect sphere out of a bar magnet, how will it choose a north and a south pole?
Asked by: Chinmay Deodhar, Pune, India

The poles of the bar magnet are determined by alignment of magnetic domains, or microscopic volumes of the magnetic material in which the electron spins are substantially pointing in the same direction. The magnetic domains are essentially tiny magnets, each with a north and south pole. They are present in non-magnetized magnetic materials, but their poles are pointing in random directions, thus canceling each other's minute fields so that there is no external magnetic field. When the material is magnetized, usually by applying a high intensity pulse from an external magnetizing field, many of the individual domains rotate so that they are aligned with the external field. This alignment takes energy to overcome the mechanical resistance of rotating the domains, as well as adding energy to the magnet by increasing the order from the random arrangement to the aligned arrangement, i.e., a reduction in entropy.

The resistance to aligning the domains is also what keeps them from spontaneously returning to their original random state when the magnetizing field is removed. This is true in so-called "hard" magnetic materials versus the "soft" materials, which retain very little of the impressed magnetic field.

From this explanation it is seen that the orientation of the poles is contained in the physical alignment of the domains in the original bar magnet. The direction of the poles will therefore be retained in sphere relative to its orientation in the unaltered bar.

The result would be quite different if the magnetic dipoles were composed instead of free monopoles, analogous to electric charges. If a conducting sphere were charged with an excess of electrons, their mutual repulsion would cause them to move and distribute evenly over the surface of the sphere, resulting in no electric "pole" at all.
Answered by: Scott Wilber, President, ComScire - Quantum World Corporation

Simple - it keeps the same north and south directions that it had when it was still part of the bar magnet. You can think of the bar magnet as being made up of a whole bunch of really really teeny bar magnets. The bar magnet gets its overall magnetization because all of these little component magnets are pointing in the same direction, and add up for an overall effect. So when you carve out your sphere, all the little teeny parts are still going to be in line with each other, and still be pointing the same way they were when they were part of the rest of the bar (unless you change their direction by spinning the sphere after you remove it).

Some people might be bothered by this description because they have been told that there are no "magnetic monopoles," i.e. there are no teeny little isolated magnetic field sources. This is true, but it turns out that if you take an electric field source (such as an electron) and run it around in a circle (say as if it were orbiting an atom), it then exhibits a magnetic moment, and looks a lot like a little magnet. These are the little magnets that I was referring to.

The next logical question might be, "well, if all it takes is electrons orbiting atoms to make up a little magnet, then why isn't everything made up of atoms magnetic?" The answer is that in a lot of cases, the teeny little magnets cancel each other out. One way they can do this is if you have two electrons orbiting a nucleus, only in opposite directions (i.e. one clockwise, one counterclockwise). Another way that magnetic fields cancel out is if the teeny bar magnets in a material are free to jiggle around in the material, and they become randomly oriented - then on average you have the same number pointed in one direction as in the opposite direction, and you get no overall effect. It's only in some special kinds of materials that you can get all the little bar magnets pointing in the same direction, and then "freeze" them there. These materials are then called magnetic materials, for obvious reasons.
Answered by: Gregory Ogin, Physics Undergraduate Student, UST, St. Paul, MN

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