# Electromagnet

Q:
I no an electromagnet works by having current flowing though a coil of wire but I was wondering why this creates a magnetic field?
- Kate (age 16)
New Zealand
A:
This is a very deep question. I’ll give a sort of superficial version of the deep answer.
First, let’s ask what a magnetic field is. We say that a magnetic field is present when electrically charged particles feel a force which depends on how fast and which way they move.
Now a current in a wire consists of a batch of moving charged particles- say moving negative electrons- in a background that keeps the total charge in the wire zero. We say then that it doesn’t exert electrical force on its neighbors. Why then should a neighboring charged test particle experience a force that depends on how it is moving? The answer lies deep in Einstein’s Special Relativity. From the point of view of the test particle, the spacing between the charged particles inside the wire depends on how fast they’re moving with respect to it. So if, according to us, the test particle is moving along with the ones in the wire, it sees a different density of charged particles in the wire than it would if it were moving, say, the opposite way. So the moving particle feels (according to it) a different electrical force depending on how it moves, with respect to us. If there were no current in the wire, then the effect would go away- the test particle would see the same density of positive and negative particles regardless of its motion.

I know that sounds complicated, but if you draw pictures, you can see how it works. There’s a nice description in a book by Purcell on Electricity and Magnetism. Of course, the real mystery lies in why distances look different to observers moving with respect to each other. All I can do is recommend any beginning text on Special Relativity.

Mike W.

(published on 10/22/2007)

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