# Simple magnetic forces and angular momentum conservation

1. Nov 2, 2010

I was thinking about internal torques and why they cancel, and I can't figure out how torques from magnetic forces cancel.

Say you have two point charges moving with nonparallel velocities. The magnetic forces they exert on each other are opposite and equal, but they aren't along the line between the two charges, so their torques don't cancel in general.

This is worrying to me because it means that their angular momentum could change without an external force, which seems wrong. Could someone please show me where I'm going wrong?

2. Nov 2, 2010

### K^2

There really shouldn't be a force in any direction other than along the line connecting two particles. But yeah, I get the same thing. If the velocities aren't parallel, I get non-zero net torque on the Lorentz Force.

I'm really not sure what's going on, but keeping in mind that both of these charges are going to be accelerating due to the forces they apply on each other (especially with non-perpendicular velocities) there is also going to be radiation from each of the charges, which might provide recoil sufficient to offset this difference.

3. Nov 2, 2010

### Staff: Mentor

The linear momentum of the particles in an electromagnetic system is also not conserved, in general. In order to regain conservation of linear and angular momentum, you have to include the linear and angular momentum of the E and B fields themselves.

4. Nov 2, 2010

### Meir Achuz

You are describing the Trouton-Noble experiment, which tested special relativity.
In fact the angular momentum of the two charges increases, but there is no tendency to rotate.. Try <http://arxiv.org/PS_cache/physics/pdf/0603/0603110v3.pdf> [Broken]

Last edited by a moderator: May 5, 2017