# Direction of vector precession

1. Oct 15, 2009

### bluestar

Not a homework question!

Consider a proton and coordinate system immersed in an upward pointing external B-field.
If the orbital magnetic number m (sub l) is a positive hbar then the vector precesses counter-clockwise about the positive z axis.

1. If m (sub l) is a negative hbar then does the vector precess clockwise around the negative z-axis?

2. What about when m (sub l) has a vector length of sqrt 6 and a 0 hbar orientation. Which direction does the vector precess?

2. Oct 19, 2009

### Prologue

1. It depends on your perspective. If the first scenario is looked at from the positive z direction and looking down at the origin, then let's agree to always keep that orientation when we give our final conclusion for the direction of precession. With this orientation the precession is counterclockwise when the angular momentum is positive.

When you look at the one with negative angular momentum it precesses in the counter clockwise direction while looking from above, too.

Why? Consider the first scenario where the angular momentum points at you (more or less) in the positive z direction but now let's flip the B field. The precession changes to clockwise because of the opposite direction of the B field. But this situation (spin up, B down, +z viewing point) is identical to you looking from the bottom toward the origin in the initial configuration (spin down, B up, -z viewing point) - i.e. in this configuration the vector precesses clockwise to the observer. But if we switch back to our initial viewing point, the positive z, and leave the B and spin alone, the precession will be counterclockwise from our viewing point.

The logical progression would be this:

(proton, spin up, B up, +z viewing point) - counterclockwise
(proton, spin up, B down, +z viewing point) - clockwise
(proton, spin down, B up, -z viewing point) - clockwise
(proton, spin down, B up, +z viewing point) - counterclockwise

If you change to an electron the precession will be opposite in all situations to that of the proton.

You can see that changing the angular momentum doesn't change the precession. But changing B, your perspective, or the sign of the charge does change the perceived precession.

2. If you look at the torque on a proton you will see that the resultant precession is the same as above, counterclockwise. All protons precess in the counterclockwise direction when viewed from above if the B field is pointing at you.

If you would like an intuitive mind model for figuring out the torques due to angular momentum, check out this excerpt from an old physics book.

http://img53.imageshack.us/img53/7207/angularmomenscan2xj4.jpg [Broken]

Last edited by a moderator: May 4, 2017
3. Oct 20, 2009

### bluestar

Wow, what a great explanation.
You have helped tremendously.

I now see my error; I was trying to apply the right-hand rule to the magnetic vector instead of the direction of the orbital charge. Your suggestion about electric loop and torque examples cleared the question.

You mentioned the vector direction of the electron was opposite of the proton, which makes sense because of the reversed charge. Likewise, I would expect the neutron to be similar to the electron because of the negative internal charge structure. Would you agree if this were considered at the nuclear level?

Thanks Prologue, I do appreciate your help.

4. Oct 22, 2009

### Prologue

Good question that I don't really have an answer to. I pretty much don't know anything about neutrons. But it is made of one up (+2/3 e) and two down quarks (-1/3 e) which are the 'givers of charge'. Since there are two down quarks maybe they spend more time on average toward the 'outer bounds' of the neutron compared to the up quark. And this would mean they have the morer angular momentum of average compared to the up quark. That would end up with a magnetic moment like that of an electron.

This is all just random speculation though. Fitting of data.