# Magnetism and the violation of the law of angular momentum

1. Nov 6, 2011

### CHUKKY

Ok they say a magnetic force can never do work on an object.ok but can anyone explain this to me? a particle is set in a velocity in the x direction, magnetic field in the y direction so dat the resultant magnetic force be in the z direction at this instant. Hence the particle moves in a circle of the field was uniform. Ok fine. What if we have a varying magnetic field what happens? the radius of instantaneous circular motion should be increasing right by the formula.This is from the formula:

F= q*v*B = mv^2/r so dat solving you get r = mv/(q)(B)

Hence as B varies r varies as well.kk if that is the case then if v is constant even while B varies, then how do we conserve angular momentum. Yh the case is made that a magnetic field always acts perpendicular to the velocity. This means angular momentum is not conserved since r is varying and m and v are constant. Angular momentum = mvr. Ok if we decide to conserve angular momentum then v has to vary. if v varies then how did v vary since magnetic forces act perpendicular to v. Now the funny thing is that i derived a formula for magnetic force dependent solely on r. I ensured that momentum was conserved in this derivation. I also made the assumption that the magnetic force is conservative so it is path independent. The funny thing is that when integrated this new formed formula with r i got exactly the change in kinetic energy expected if angular momentum was conserved. So people my question is this what is happening:
is angular momentum conserved or not?
if not how does a particle change kinetic energy since magnetic field can do no work becos it always acts perpendicularly to the velocity. People this baffles me a lot. I would appreciate your answers

2. Nov 7, 2011

### Phrak

The changing magnetic field is accompanied by an electric field so Ampere's law should be used.

3. Nov 7, 2011

### Simon Bridge

But you set the situation up so that B also varies.

Imagine a particle curves from a region (1) with field strength B to a region (2) with strength 2B in the same direction. Then, from your equation, $r_1=2r_2$.

$p_1=qBr_1 = 2qBr_2 (=mv)$
$p_2=q(2B)r_2 = 2qBr_2 (=mv)$
... identical.

@Phrak: aren't you thinking of a time-varying B field?
That would also make the path vary, as well as change the kinetic energy via the accompanying E field.

Last edited: Nov 7, 2011
4. Nov 7, 2011

### Phrak

That seems to be what he's asking about, as r changes in his second scenario. Make that Faraday's law.

5. Nov 7, 2011

### CHUKKY

So that means that the change in momentum is not as a result of the magnetic force but as a result of the electric force that results from time varying magnetic field? right?

6. Nov 7, 2011

### Philip Wood

Chukky. First, thanks for the question: interesting and nicely explained.

Why would you expect the particle's angular momentum to be conserved? It's not an isolated system. The complete system would be the particle and (say) a coil with a changing current through it, to generate the changing B. We must take account of the angular momentum changes of the electrons in the coil as the current through it changed.

I agree that the interaction between particle and coil is by both B and (induced) E fields.

Last edited: Nov 7, 2011
7. Nov 7, 2011

### D H

Staff Emeritus
And the electromagnetic field. The electromagnetic field itself can store energy, linear momentum, and angular momentum. Quantum mechanically, real photons (as opposed to virtual photons) are involved in a time-varying electromagnetic field, and those real photons are a part of the system. Exclude them from the system and the conserved quantities can appear to be not conserved.

8. Nov 7, 2011

### CHUKKY

Now you guys have added a different dimension to the answer. So what would happen then. Is the velocity of the particle going to remain the same through out the time in this time varying magnetic field. If it remains the same then does it mean that the change in angular momentum is conserved by the counter change in angular momentum of the electrons in the coil (or conductor). If your answer is no the velocity changes then what changes the velocity since magnetic forces always act perpendicular to the velocity vector, or is it the electric field that causes this change as Phrak mentioned?
so wat is happening?

9. Nov 7, 2011

### CHUKKY

same question to you:
Now you guys have added a different dimension to the answer. So what would happen then. Is the velocity of the particle going to remain the same through out the time in this time varying magnetic field. If it remains the same then does it mean that the change in angular momentum is conserved by the counter change in angular momentum of the electrons in the coil (or conductor) and the photons that exist in such a field as you mentioned. If your answer is no the velocity changes then what changes the velocity since magnetic forces always act perpendicular to the velocity vector, or is it the electric field induced that causes this change as Phrak mentioned? or do we solve this situation by conserving both angular momentum and energy of the system since any collision in such a conservative field is always perfectly elastic.
so wat is happening?