# Current in a wire

1. Nov 19, 2014

### Scheuerf

If a wire is neutral, and the electrons in it suddenly start to move, why is the wire still neutral? I would think that the electrons would contract causing the wire to be negatively charged.

2. Nov 19, 2014

### skeptic2

Why do you think the electrons would contract? Electrons, as far as we can measure, are point sources so how could they contract? If when current starts to flow, as many electrons leave the wire as are added to it, why would it not still be neutral?

3. Nov 19, 2014

### Scheuerf

If I'm correct, the electric fields of the electrons should contract and so should the space between them like the picture in this Wikipedia link under basis in relativity. http://en.m.wikipedia.org/wiki/Length_contraction

4. Nov 19, 2014

### skeptic2

Electrons do not travel at relativistic speeds in a conductor. In fact they travel quite slowly. It is only the wave action that travels at the speed of light. The popular analogy is marbles packed in a tube. The marbles may be traveling very slowly in the tube but any change in motion moves from the input to the output very fast.

5. Nov 19, 2014

### Matterwave

The electric fields of the electrons do sort of "length contract", but they don't do so in a simple way like you are thinking. The static electric field in the rest frame of the electrons is transformed by a Lorentz transformation, partly into a magnetic field in the rest frame of the wire.

See here for some details: http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity

6. Nov 19, 2014

### Scheuerf

But there are a lot of electrons and protons in a wire, so contracting of particles in the wire cause it to repel or contract moving charges.

7. Nov 19, 2014

### Matterwave

Particles themselves do not contract, the distances between protons do, as viewed in the frame of the moving electrons. The distances between the electrons contract, as viewed in the frame of the wire. Like I said, after everything is considered, this leads to a magnetic field being present in the frame of the wire, and will, in fact, give you Ampere's law. Because the transformed field is a magnetic field, the consequences are not so simple as they "attract or repel" other charges.

Notice in your video that the cat has to be moving in order to feel some forces. This is a direct consequence of the fact that magnetic fields don't work on static charges, but only on moving charges via the Lorentz force.

8. Nov 19, 2014

### ChrisVer

All in all the video doesn't say much but what Maxwell's equations state, just from the prespective of a simplified Special Relativity point of view, where electricism and magnetism are just one force, seen from different reference frames.
As he states, although in his reference frame there is no "free" charge in the wire, he is seeing the charged cat moving because of the magnetic field. On the other hand the cat is not experiencing a magnetic field but an electric field because it's moving.
The maxwell equations except for charges as sources of the electric field, also have the change of the magnetic field. In SR both them are unified into one quantity - the EM antisymmetric tensor.

PS personally I don't like the contraction example...it caused me a mind explosion right now...

Last edited: Nov 19, 2014
9. Nov 19, 2014

### jartsa

That would make the wire negatively charged, in the wire frame.

... So the distances between the electrons stay constant in the wire frame, when the current is adjusted.

10. Nov 19, 2014

### Matterwave

Yes, you are right. I got too sloppy in carrying out the relativistic corrections in my head. The distances between the electrons stay constant, they are just drifting along. In fact, the video mentions this as well. :)

11. Nov 19, 2014

### Staff: Mentor

On the positive side of the wire it becomes a little positively charged. On the negative side of the wire it becomes a little negatively charged. So the net charge is 0.

If you want it to be positively charged you can just raise the overall voltage. If you want it to be negatively charged you just lower the overall voltage.

Length contraction is irrelevant. The charge is determined by the voltage. This isn't to say that length contraction doesn't happen, it does and it can be used to understand magnetism. But it doesn't control the charge on the wire.

Last edited: Nov 19, 2014