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If I take a really big magnet and use it to pull a large metal object then clearly there will be a force pulling this metal object toward the magnet.

But is Newtons third law obeyed here? Will the magnet also have the same force applied to it, pulling it toward the metal object? Or will the magnet experience no force at all, and have the metal object just come toward it?

I'm comfortable with vector calculus and electromagnetism (engineering) but as far as I know there is nothing in any of my textbooks which would explain this interaction, because the magnet isn't really causing a force on the metal object... its just creating the magnetic field which attracts the object because of the magnetic field created by the metal object... which should also attract the magnet. But is Newton's third law going to hold here?

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The attraction is felt both ways: magnet to metal and metal to magnet. You can demonstrate this by instead holding the metal at a fixed location and moving the magnet slowly closer, it will suddenly jump into contact with the metal.

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