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Does a magnet lose more of it's magnetic potential when (passively) magnetizing a second (ferromagnetic) metal compared with simply being left alone for the same amount of time it took?

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A magnet does not lose any of its magnetism when it magnetises another piece of metal. Well, it doesn't necessarily lose any of its magnetism.

The lowest energy state of a ferromagnet is to have all of its magnetic domains aligned. The reason pieces of e.g. iron generally aren't magnetised is because they are stuck in a local and the individual domains aren't free to rotate their fields into alignment with each other. So when you place your piece of unmagnetised iron near a permanent magnet it does not need to take energy from that magnet. Instead it will gradually settle into a magnetised state and release energy (i.e. get slightly hotter) as a result.

Incidentally the fact a material releases heat when it becomes magnetised can be used as a cooling method rather unoriginally called magnetic refrigeration.

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