Simple magnetic forces and angular momentum conservation

[readywil]

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?

 

[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.

 

[jtbell]

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.

 

[Meir Achuz]

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?

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>

 

[sardar]

I can provide an explanation for the concept of simple magnetic forces and angular momentum conservation. Firstly, it is important to understand that magnetic forces are a result of the interaction between charged particles and magnetic fields. These forces can cause objects to move in a circular or curved path, depending on their initial velocity and the strength of the magnetic field.

In the scenario described, where two point charges are moving with non-parallel velocities, the magnetic forces they exert on each other are indeed opposite and equal. However, as you correctly pointed out, these forces are not along the line between the two charges, which means that their torques do not cancel out in general. This can lead to a change in the angular momentum of the system.

But this does not violate the principle of angular momentum conservation. As per this principle, the total angular momentum of a system remains constant unless an external torque acts on it. In the case of magnetic forces, while the torques may not cancel out, they are internal torques acting within the system. This means that the total angular momentum of the system still remains constant.

To better understand this, consider the example of a spinning top. As it spins, the internal torques from the different parts of the top do not cancel out, yet the top maintains its angular momentum. This is because the top is a closed system and there are no external torques acting on it.

Similarly, in the scenario described, the two point charges and the magnetic forces between them can be considered a closed system. While the torques may not cancel out, there are no external torques acting on the system, so the total angular momentum remains constant.

In summary, the concept of internal torques and their cancellation is not necessary for angular momentum conservation. As long as there are no external torques acting on a closed system, its total angular momentum will remain constant. I hope this explanation helps to clarify your doubts.