# Question relating to direction of magnetic force on moving charge

1. Aug 20, 2013

### parsa418

Hi
I have always been very curious if anybody knows why the magnetic force on a moving charged particle in a magnetic field is always perpendicular to the plane containing the magnetic field's vector and the charged particles velocity vector.
Any help would be greatly appreciated.
Thanks
Parsa

2. Aug 20, 2013

### Staff: Mentor

That's just the universe we live in. It could be different, but apparently it is not.

It is interesting to see that a force in any other direction would violate energy conservation.

3. Aug 20, 2013

### technician

I have never thought of it from an energy conservation point of view....this does sound interesting...can you elaborate?

4. Aug 20, 2013

### Staff: Mentor

A force component parallel to the velocity in a pure magnetic field (in our lab frame) would increase (or decrease) the energy of the particle, without any potential difference for this particle -> energy is not conserved.
A force component along the magnetic field would lead to a non-conservative force, as magnetic field lines are closed -> energy is not conserved.

5. Aug 21, 2013

### technician

Thank you !

6. Aug 21, 2013

### parsa418

A force component along the magnetic field would lead to a non-conservative force, as magnetic field lines are closed -> energy is not conserved.

Thank you for your reply. Can you elaborate a little more on the reason above. I don't understand why the magnetic field lines being closed would lead to a non-conservative force.
Thank you
Parsa

7. Aug 21, 2013

### Staff: Mentor

A force along the magnetic field lines leads to a potential drop along the field lines. You could follow that potential drop along the circular line, and arrive at the original point again - but with a lower potential. A potential cannot have two different values at the same point at the same time, so this is impossible.

Strictly speaking, we would have to include the velocity in the consideration, but that does not change the main issue.

8. Aug 21, 2013

### parsa418

I see how that makes it nonconservative. Thank you. You at least have given me a reason for why the force direction being perpendicular to the v-B plane would have made the most sense (or at least special) because it would have violated energy conservation if it wasn't in that direction.
Thank you

Last edited: Aug 21, 2013