# Magnetism results from relativistic effects on a moving charge?

1. Jul 17, 2007

### Leon31415

Hi

Does anyone have a link to a proof that magnetism is a result of relativistic effects on a moving charge? I am sure that I have seen one but I cant find it.

Thanks

John

2. Jul 17, 2007

### StatusX

I don't have a link, and I don't know what you mean by a proof, but here's a rough argument. Because of length contraction, the charge density of an object increases as $\gamma$ with velocity, and so it's electric field changes as well. In order for different, relatively moving observers to observe the same force, there must be an extra term coming from the movement of the object, which is the magnetic field.

For example, say there are two uniform, parellel line charges of opposite signs. Then they attract with a certain force. Now if we transform to a frame moving parellel to the wires, their lengths contract, so the charge density increases (since total charge is invariant under lorentz transformations). Thus we should expect the wires to pull on each other more strongly, which would contradict the prediction of the first frame. This effect is counteracted by fact that the magnetic fields of two parellel wires of oppostie current are such as to repel the two wires, and so the predictions come out the same in both frames.

This is an argument that what appears as an electric field to one observer will appear as a magnetic field to another. This together with a proof that Maxwell's equations are lorentz invariant are really the closest you can come to the proof you want.

3. Jul 17, 2007

### pervect

Staff Emeritus
I'd suggest the wikipedia article http://en.wikipedia.org/w/index.php?title=Relativistic_electromagnetism&oldid=145189916

and it's reference
http://physics.weber.edu/schroeder/MRR/mrr.html

If you want a well-known peer reviewed textbook source, get a hold of Purcell's book on electromagnetism.