Why does Larmor precession appear to go against the right hand rule?

[kmm]

For some reason, I don't understand the direction of larmor precession. Torque is: $$\mathbf{\Gamma} = \frac{d \mathbf{L}}{d t} = \mathbf{r} \times \mathbf{F}$$ As an example, I understand with a gyroscope, using the right hand rule and with angular momentum in the direction as shown in this picture, it will precess counterclockwise looking down on it.

Now, with larmor precession, the torque is: $$\mathbf{\Gamma} = \frac{d \mathbf{L}}{dt} = \mathbf{\mu} \times \mathbf{B}$$ From the right hand rule, the torque is in the opposite direction as that of the gyroscope so the change in angular momentum should give a precession clockwise. But in the image below, and every other image I've seen, it still goes counter clockwise in the opposite direction of the change in angular momentum. Well, I have found on other sites that the change of angular momentum is in the opposite direction I get from the right hand rule. I'm not sure what I'm doing wrong. Thanks!

 

[Pythagorean]

Could it be a matter of charge?

 

[kmm]

Could it be a matter of charge?

Except the charge is taken into account in the direction of the magnetic moment.

 

[Dale]

Interesting. I looked at my MRI textbook (Haacke, et al. 1999. Magnetic Resonance Imaging: Physical Principles and Sequence Design). On p 29 it has a drawing with the correct direction of precession. It looks very similar to the plot you are showing, but precessing CW. I don't know what source you are using or why it gets the sense backwards, but it seems to be a mistake in your source rather than a consistently different convention.

 

[kmm]

It looks very similar to the plot you are showing, but precessing CCW. I don't know what source you are using or why it gets the sense backwards, but it seems to be a mistake in your source rather than a consistently different convention.

My expectation by the right hand rule is that it should precess clockwise. But yes, all the sources I've seen showing larmor precession show counter clockwise precession, agreeing with your textbook. Did you mean yours shows clockwise precession?

 

[Dale]

Yes, I meant CW. I edited it, but not before you caught the mistake.

My textbook shows the correct direction which is opposite the direction of your picture.

 

[kmm]

Could it be a matter of charge?

Actually, I think Pythagorean was right. The sources I was looking at are referring to electrons or negative charges so the magnetic moment vectors I was looking at are actually negative so the magnetic moment $\mathbf{\mu}$ had a negative value, flipping the direction of the torque.

 

[Dale]

That could be. My text is a MRI text, so the spins of interest are protons rather than electrons.