# Infinitely long magnet

1. Dec 6, 2007

### tomprice

Ok lets say we have an infinitely long magnet, with poles arranged like in the diagram. A positively charged particle is moving as shown in the diagram. Because of Lorentz forces, the particle will be accellerated towards you. Now change the frame of reference so that the particle is stopped but the magnet is moving. Due to the translational symmetry of the magnet, the magnetic field is not changing at any point. So, what is it exactly about the magnet being moved that has any effect on the stationary charged particle?

<- NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN ->
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

(charged particle moving right) o ->

THank you very much!

2. Dec 7, 2007

### dst

If the magnet moves, then the magnet is doing work. That work has to be converted into another form of energy. Since your magnet is infinitly large, it's an impossible scenario because you would need the magnet to do infinite work to even move.

Also, with an infinitely large magnet, you would have an equally infinite force on the charged particle (at least, intuition tells me), or at the very least, equal to the total force within the event horizon.

3. Dec 7, 2007

### tomprice

Ok let me clarify my question.
If the magnet is stationary, no force will be exerted on the charged particle, supposing it stationary as well. (Let's ignore gravity, or suppose the magnet is massless, or something like that...)

If the magnet is moving along the axis of infinite length, a force will be exerted on the charged particle, equal to the velocity of the magnet times the magnetic field at the charged particle times the charge of the particle. (F = qvB)

Since the magnetic field is still acting just how it did with the stationary magnet (due to translational symmetry), it can't be directly responsible for this force. So, there must be some other sort of field or effect or something that is caused by the moving magnet.

What is the name of it? What is the nature of it?

The fact that it is impossible to construct the infinite magnet, or get it to move (though like I said, it doesn't take too much energy to get the charged particle moving, then just change your frame of reference...) is not relevant to the question.

Thanks again.

4. Dec 7, 2007

### Staff: Mentor

It sounds like you are interested in what a magnetic field looks like in another reference frame. Essentially, in relativity you realize that space and time are not completely independent, but are separate components of spacetime. Similarly with momentum and energy, and electric fields and magnetic fields. They are different names for the same thing as seen in specific reference frames.

That is a long-winded way of saying that as you boost a magnetic field you start to get an electric field and vice versa. Try this page for starters: http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html

Last edited: Dec 7, 2007
5. Dec 8, 2007

### tomprice

Thanks for the link, it was interesting.

So does this mean that, whenever you have an electrical current flowing through a wire, the wire gets a slight negative charge due to relativistic length contraction?

6. Dec 8, 2007

### Staff: Mentor

That depends on the reference frame in which you are analyzing the situation. In some reference frame the wire is uncharged, there is no electric force, only a magnetic force. In other frames the wire will be slightly charged and so there will be an electric force. The net result is that all frames predict the same force, although they will disagree about how much is due to E and how much to B.