# [Physics] Why does an electromagnet attract iron according to Special Relativity

electric-fieldselectromagnetismmagnetic fieldsspecial-relativity

I saw a video of Veritasium on "How Special Relativity Makes Magnets Work" and came up with a question. So please watch the video first before answering my question as it is related to the video.

1) If Instead of that positively charged cat we use an iron nail (which is also moving in sync with the current like that cat which was moving previously), the iron nail gets attracted to the electromagnet. But why does it get attracted to the electromagnet in the iron nail's frame of reference? In the cat's case we can accept it because like charges repel but why in iron nail's case – it is not charged.

2) If a changing electric field creates a magnetic field (according to our frame of reference) then how do you determine the north and south pole of an electromagnet?

If Instead of that positively charged cat we use an iron nail (which is also moving in sync with the current like that cat which was moving previously),

You are asking what if you had a stationary neutral wire with a current and you moved a piece of iron so that it moved at the rate the mobile charges moved why would it react?

If you go back to the case of the charged cat. In the frame of the cat it is just at rest, seeing a net charge and some stationary electrons and some moving protons. And since it is at rest it only sees electric effects, so the current of the protons doesn't matter, only the electric charge imbalance matters.

But for the iron, it is intrinsically magnetic because each electron is intrinsically magnetic and the electrons can line up in a shell for each iron atom to make a dipole moment for the atom, and the atoms in a domain can line up to make a domain full of a large dipole moment per cubic meter and the domains can line up if the history of the iron in the past forced them to line up through an external field.

And this means it cares about magnetic fields. And it does so in a 100% completely different way than charges care about magnetic fields. It straight up had the magnetic moment directly interact with the magnetic field.

If a changing electric field creates a magnetic field (according to our frame of reference) then how do you determine the north and south pole of an electromagnet?

The north and south pole of an electromagnetic are unrelated to changing electric fields. You can have a steady current and get unchanging electric fields and still have a current and have magnetism.

Changing electric fields simply act like an additional current (called a displacement current) allowing magnetic field to circulate without needing an actual charge. Or alternatively you could say that when the circulation of an magnetic field does not match the actual current it causes the electric field to change.

The north and south poles of electromagnet is determined by the direction the wires wind around and the direction the current flows through a wire.