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Suppose your have any magnetic object and no external force acts upon it, and the object comes near a metal which causes an impulse (think that will happen). However, the magnetic force is internal to the object, and momentum should be conserved, so where have I gotten it wrong?

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There is a corresponding reaction force on the metal object, which is attracted to the magnet. If the metal object is large (say, a fridge) then this is hard to notice and you observe the magnet going to the metal, but for smaller objects like paper clips it's the opposite.

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