# Relativity of E & M question

1. Apr 18, 2012

### omega_minus

I have seen quite a few times the argument about a wire carrying current and a charged particle outside the wire. When the particle is at rest with the wire it feels no force, since the magnetic force on the wire requires relative motion of the particle and the field. It also feels no electric force since the wire is electrically neutral. When the particle moves along the wire it then is accelerated toward (or away) from the wire. In the lab frame of reference its due to a magnetic force but in the particle/current frame its because now the charge densities of the conductor have changed. Here is my question: From the lab frame the electrons carrying current have *somehow* lowered their charge density to a lower amount in their frame so as to appear to the lab frame (once Lorenz contracted) that the wire is neutral. I have read that this is because any excess static electric field would be neutralized by the electrons in the wire. However these explanations never bother to say why the electrons have "decided" to make the wire neutral in another frame of reference and not their own. It seems like they always "want" the rest frame of the wire to appear neutral. Why don't the electrons arrange themselves to make the wire neutral in their own frame? What makes the frame they now travel in so special that they would allow a static field to exist there but not try to neutralize it?

2. Apr 18, 2012

### Staff: Mentor

It isn't the electrons that want the wire to be neutral, it is the experimenter. He does so by not applying a high voltage to both ends of the wire.

If the experimenter wanted to charge the wire in his frame so that it was neutral in the drift frame of the electrons then he could do so simply by applying a high voltage to both ends of the wire (in addition to the small voltage difference across the wire).

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