ANSWERS: 4
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Depending how it's cut it will definitely lose some magnetism but no it shouldn't lose all.
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No, what you end up with is two magnets each with a half-horseshoe shape. In a permanent magnet, the atoms are aligned in such a way that their individual magnetic fields reinforce. Even when you physicaly cut the magnet, those atoms are still aligned on the microscopic level. In order to demagnetize a magnet, the atomic magnetic fields need to be randomized. One way to do this is to heat the magnet above its Curie Point. http://en.wikipedia.org/wiki/Curie_point
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A couple of different things can happen when you cut a magnet in half. If you do it gently you can end up with two magnets. You can think of a magnet as a bundle of tiny magnets, called magnetic domains, that are jammed together. Each one reinforces the magnetic fields of the others. Each one has a tiny north and south pole. If you cut one in half, the newly cut faces will become the new north or south poles of the smaller pieces. You could keep slicing smaller and smaller slices like a loaf of bread and keep getting thinner magnets, each with a new set of poles. Remember, I did say though you only get two magnets if you cut them gently. The magnetic domains in a magnetic material can be knocked loose, by bumping or vibrating the magnet (like when sawing it in half). If knocked loose, the domains are no longer arranged neatly, so they do not reinforce each other. If they are in a random orientation, with their fields pointing all over the place, they cancel each other out. http://tinyurl.com/33dt3q
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Irrespective how many pieces of any magnet, of any shape is done, each piece will be a new magnet. Coming to horse shoe magnet, the two pieces will be a new magnet.(having north & south pole).
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