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Question:

Would melted iron be attracted to a magnet? Why?

If iron is melted and then a powerfullt;electromagnet brought near it, will the iron be attracted towards the magnet.

Answer:

Yes, but not as strongly. Above the Curie temperature, iron is no longer ferromagnetic, but it is still paramegnetic. Molten iron cannot maintain a permanent magnetic orientation.
No Idea but taking an educated shot in the dark here i would say YES. Saying YES because although in the liquid/molten form where the electrons a freely roaming and sliding pass each other in a definite space, if an electromagnet powerful enough can be found that can still align those electrons then it is possible that even in the molten state Iron would be magnetic
No way a magnet can attract liquid iron. Look, iron is ferromagnetic and that's why it is attracted by magnet(which is also iron and difference between normal iron and magnet is that, magnet is magnetically ordered, i.e. all electron spins are aligned in SAME direction). When a magnet comes near to a normal iron, it forces the irons electron spin to be aligned in such a way that they attract each other. Now, irons melting point is much higher then its Curie temperature and hence presence of a magnet cant make the electrons aligned in any direction and hence, melted iron wouldn't be attracted by magnet.

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