# Does a charged particle rotate when traveling through a static Bf?

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1. May 19, 2013

### mesa

I have been looking at mass spectrometers, in particular the interactions between the Bf ind of a charged particle in motion in a static Bf of the spectrometer.

Figure 1 and 2 shown below are a basic 2 dimensional slice of the problem from the top (fig 1) and from the inside of the radius looking out (fig 2) to establish our F.o.R.

Figure 3 is a view of the charged particle moving towards us at velocity vq- with the 'direction' of the Bf ind shown along 8 symmetrically spaced points.

[URL=[PLAIN]http://s1332.photobucket.com/user/ian5576g/media/crossproductpage1_zps8daf6515.jpg.html][PLAIN]http://i1332.photobucket.com/albums/w606/ian5576g/crossproductpage1_zps8daf6515.jpg [Broken]

Figure 4 below shows the interaction of the Bf ind with our static Bf along these 8 points and the resultant Force at those points. Figure 5 uses this information to draw a 'representative' magnitude for the Force along different points acting on our moving charged particle in the static Bf. To me this looks like the Force at these points would mediate a rotation about an axis drawn through a charged particle in the direction of 'y' if moving through a static Bf as shown, is this correct?

Last edited by a moderator: May 6, 2017
2. May 19, 2013

### Simon Bridge

You diagram appears to assume a uniform spherical charge distribution for the charged particle or a planetary model for an atom. Real charged particles are more complicated than that but this is a good effort - well done.

Charged particles that have a non-zero magnetic dipole moment (look it up) will rotate in a magnetic field - yes.

3. May 20, 2013

### mesa

I was thinking the particle as being a single electron or proton moving through a static Bf. Will they rotate in a mass spectrometer as well?

4. May 20, 2013

### Simon Bridge

5. May 20, 2013

### mesa

So this rotation creates only one of two states leading to the discovery that electrons in motion behave like a dipole as shown by a modified Stern-Gerlach Experiment.

I have been drawing this one up but am not seeing how a rotating Ef would create a dipole perpendicular to that of the motion. Should I look at it from the standpoint of the rotating Bf ind of the particle instead?

6. May 20, 2013

### Simon Bridge

In the classical image, the charge of the particle is thought of as being distributed in space - much as you drew.
Recall that moving charges are an electric current, and an electric current has an associated B field.
If the charge distribution is rotating, then the charge element a distance r from the axis of rotation is moving in a circle - so it is a current loop - so it is a little electromagnet. Since all the charge elements rotate the same direction, they add up.
You can do the math for a rotating sphere of charge Q and radius R if you like.

But the math doesn't agree with experiment.

The modern description is statistical - via quantum mechanics.
A particle may have a non-zero magnetic moment as if it were spinning - but we do not imagine the particle actually spinning ... more that it "carries" angular momentum with it much as it may carry linear momentum and charge and kinetic energy and so on.

If a particle has angular momentum and charge, then it also has a magnetic dipole moment.

The reason I brought this up is that you have managed to explore a bit of theory where the model you are using is not adequate to the task... so you have just hit the next level. It will feel very strange for a while but you get used to it.

What you have been doing would be appropriate for a classical charged insulator fired through a B field rather than a fundamental particle.

Last edited: May 20, 2013
7. May 21, 2013

### mesa

I got past the sticking point from yesterday, nice to see your suggestion is in line with it. The figures above are illustrating a point charge in motion with the Bf ind some distance 'R' from it giving me trouble spotting a dipole induced by a rotation of an electron.

I redrew the problem with a distribution of charge for an electron from the point of view of the surface so that it is easier to see how a rotation will induce a dipole. Unfortunately (as you pointed out here) it seems the Stern Gerlach experiments show that the dipole can only face in one of two possible directions which wouldn't make sense for this type of system.

So QM uses angular momentum but there is no actual rotation? This should be fun although I still have more to explore in classical mechanics before diving into the deep end of the pool. Thanks for the help, I should probably not add any more to this thread as I have already strayed far from the initial topic.

8. May 21, 2013

### Simon Bridge

What QM does is tell us that the phenomena that we classically label "angular momentum" may not always be sensibly talked about in terms of the phenomena that we classically label "rotation".

We don't think of an electron, say, as physically spinning any more than we think of an electron in an atom as physically "orbiting" the nucleus like a planet... although we do say it has orbital angular momentum.

It is possible to fire a whole bunch of particles with the same "spin" at a macroscopic object - thus transferring angular momentum to that object, to see if it tries to rotate. And it does.
Maybe this means that the particles are actually" spinning? But how would you tell?
It just doesn't make sense to talk about what a particle is "actually" doing.

But it is exciting to think that you are at a place in your studies now where you are hitting the limits of what conventional knowledge can deal with. Have fun - there's lots to be had :D

9. May 21, 2013

### mesa

Amazing, so even though QM says there is no actual rotation when it is brought back into the macro the behavior reverts to classical physics. WOW!

I can't wait! I took this summer off to spend more time with my kids and dig deeply into the previous semesters topics while preparing for what is to come.