Lorentz Force & Frame Changes: Explaining E & B Fields

[cragar]

Lets say in frame 1 I have a neutral current carrying wire that has a +x line charge and a -x line charge and they have a relative speed between them. So In frame 1 there is only a B field. And in frame 1 we also have an electron moving with respect to the wire, so the electron is deflected because of the Lorentz force. Ok now we look at it from the electrons rest frame, called frame 2.
In frame 2 there is now an E field because the charge densities have changed because of length contraction. But in frame 2 why couldn't I say that the B field is moving toward the electron and that is why it got deflected. Like if I had a square loop of wire and It was moving at a constant speed into a region with a B field. When the square loop entered the B field, electrons will start to flow because of the Lorentz force. But if I look at this in the square loops rest frame it would appear that the region with the B field is moving towards the loop. Why do I need to talk about an E field. I know there is no force if v=0 but it seems like we have a relative speed in both cases.

 

[Valerie Park]

A:In frame 2 the electron is at rest and the current carrying wire has a length contracted in the direction of motion. The electrons that are moving in frame 1 which causes the B field, have a shorter path to travel in frame 2 and therefore there is an excess of positive charge on one side of the wire, and an excess of negative charge on the other side. This excess of charge cause the E field in frame 2. This is why you need to talk about the E field. The E field is what causes the Lorentz force on the electron.