# Precession of 1/2 spin particle

1. Nov 9, 2015

### nmsurobert

1. The problem statement, all variables and given/known data

A beam of spin 1/2 particles with speed v passes through a series of SGz devices. The first SGz device transmits particles with Sz = ħ/2 and filters out particles with Sz=-ħ/2. The second SGz device transmits particles with Sz=-ħ/2 and filters out particles of Sz=ħ/2. Between the two devices is a region of length l in which there is a uniform magnetic field B pointing in the x-direction. Determine the smallest value of l such that exactly 25% of the particles transmitted by the first SGz Device are transmitted by the second device. Express your result in terms of ω=egB/2mc and v.
2. Relevant equations

3. The attempt at a solution

Because of the way particles are being passed through the two SGz devices doesn't only 25% of the particles pass through the second device regardless of the distance between the SGz devices?
I know that's not exactly right but I'm failing understand why it's not right.
I've been pulling my hair out. I have no idea where this 'l' variable is coming from.
Any advice or direction would be appreciated.

2. Nov 9, 2015

### TSny

Make sure you're not thinking of the B field in the x direction as acting like a SGx device.

3. Nov 9, 2015

### nmsurobert

I don't think I'm thinking of it as an SGx device. So the magnetic field just changes the spin over time, right? But that's for B in the z-direction. Does B in the X-direction do the same thing?

4. Nov 9, 2015

### TSny

As the particle passes through the Bx field, the field alters the spin state of the particle. You need to know specifically what the Bx field does to the spin state. The net change in the spin state due to the Bx field depends on how much time the particle spends in the field. That's why the distance L matters.

5. Nov 9, 2015

### nmsurobert

Ok. I understand why it's important. Butbim having trouble finding an 'l' anywhere in my book or notes. I don't know where the variable is supposed to be derived from.
Is 'l' an angle? That's all I can find in relation to the equations given at the end of the problem.

6. Nov 9, 2015

### nmsurobert

Thank you for your help thus far btw.

7. Nov 9, 2015

### TSny

In this font, lower case L looks too much like upper case I. Is it OK if we use 'L' instead of 'l' for the distance the particle travels through the uniform field Bx? L is not an angle, it's a distance. Can you relate the time, t, that the particle spends in the region of Bx to the distance L?

8. Nov 9, 2015

### nmsurobert

Well if it's moving at speed v and v = change in distance/time. And L is the distance we're trying to measure. There's a relation I suppose.

9. Nov 10, 2015

### TSny

As preparation for this problem, you should have studied what happens to the spin of a particle when placed in a uniform magnetic field.

Last edited: Nov 11, 2015