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Can a magnet be cut with a hacksaw, by hand, without losing its essential characteristic of being magnetic? I know i would have to be very careful with heat but I don't know how careful

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If heat is a concern, then liquid nitrogen will make it a snap! –  Arjang Dec 26 '12 at 2:35

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This would likely mess up the polarity of the magnet near the area where you are cutting. It would depend on several factors, namely how big the magnet is compared to the hacksaw blade (the bigger the magnet the more likely you are to preserve it) and what the magnet is made out of, for instance if the magnet is steel then it would definitely deteriorate the field significantly, but if it were iron and it would not be as degrading because the atoms hold their polarization better. It would have no effect on an electro-magnet.

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