Stern-Gerlach experiment questions

[Pet Scan]

In the Stern-Gerlach experiment , they used silver ions with a an unpaired electron in the outer shell...The typical result from passing the silver ions through a Non-uniform magnetic field is to separate spatially the bean into two types of "spin"...In other words the non-uniform B filed cause a force component to act in the direction of the field gradient.
But didn't the particles have a net charge?? If so, why didn't the Magnetic field cause the usual Lorentz force to cause typical curvature in the beam trajectory perpendicular to the B field lines?
Here's the picture of the exper. set-up:
https://www.google.com/search?q=ste...=dT3HV8iJM4TzmQHXzYzIDA#imgrc=sFRcsxTcpjBfCM:

Thanks.

 

[Doc Al]

No, the silver atoms were not ions and had no net charge. They did have an unpaired electron in the outer shell.

 

[Pet Scan]

Thanks Doc; but how is it possible to have unpaired electrons with no net charge.??

 

[Doc Al]

Thanks Doc; but how is it possible to have unpaired electrons with no net charge.??

The charge just depends on keeping the number of protons equal to the number of electrons. Having an unpaired electron has nothing to do with that.

All the other electrons (the inner 46 electrons) are paired off and thus have their spins (and magnetic moment) canceled. That single unpaired electron does not get "canceled". That's what creates the effect.

 

[Pet Scan]

Makes sense...thanks for the explanation.

 

[Pet Scan]

Doc Al; I still need help...
In continuation of Stern Gerlach type experiment, I was hoping you (or someone) could answer a few more questions:
In Stern-Gerlach the magnetic dipole (associated with the silver atom) experienced a lateral force (perpendicular to its velocity) . This force was proportional to the spatial gradient of the magnetic field .
1. Considering the internal energy, W, and the interaction with the field gradient, what is the general equation for a mag . dipole in a field gradient?
Is it ... F= dW/dB * dB/dx ...where dB/dx is the spatial gradient.
Or should I be looking for the force in terms of the magnetic moment , u, of the dipole ...WHAT WOULD BE THE EQUATION of motion in that case??
After that I have one more question...
Thanks

 

[Doc Al]

There's a pretty good discussion of it here: Stern-Gerlach Experiment

 

[Pet Scan]

Yes, Thank you again, Doc; I had seen that link before and forgot to check the eqns...It is a good description of the magnetic moment dependent Potential energy eqn. and the force equation...exactly what I needed to review...

Now I can go to my final question which brings out the whole purpose of this thread in the first place.
I now want to change the Stern-Gerlach exper. situation somewhat . Let us take the situation where I am sending a classical magnetic dipole NOT with uniform velocity, but ACCELERATING it, let's say, mechanically (not electromagnetically)... through a UNIFORM magnetic field. This will be a "charge free" classical magnetic dipole (free to rotate) that will be mechanically ACCELERATING perpendicular to the B field but this time through a UNIFORM homogenous magnetic field. [ All with non-relativistic speeds].

(Equivalently, I could simply let the magnetic dipole be stationary and uniformly accelerate a homogenous B field of a long Stern-Gelach type apparatus against the dipole.)

Now here is the question:
1. Classically, In the dipole's accelerated frame does it experience a spatial Gradient of the magnetic field because it is accelerating?? IOW, does it see a dB/ dx in its accelerated direction...and how do I determine what that gradient is? OR does it experience in its frame a TIME DEPENDENT change in B field due to its acceleration??

AND 2. If it does experience a field gradient, how can I modify the eqns. you gave in the previous link to account for changes in the dipole potential energy and the magnetic moment so that I can calculate the force eqn.?
I suspect there should be an acceleration equation derivable in terms of either the B field gradient or the gradient of the potentials...or if it involves a time dependent B field change, it should involve Maxwells equations., no?

Any thoughts you can give me on each of these points would be greatly appreciated...(since I know you have expertise in these areas)...especially with regards to how to acquire the force eqns. in this situation.
Thanks for the help.

 

[Doc Al]

Not sure why you think such a particle would experience a field gradient as it moves (whether accelerating or otherwise) through a uniform magnetic field.

 

[Jilang]

Huh? Isn't the field in the Stern Gerlach experiment inhomogeneous?

 

[Doc Al]

Huh? Isn't the field in the Stern Gerlach experiment inhomogeneous?

Of course. But a different scenario (with a uniform field) was proposed in the post above.

 

[Pet Scan]

Not sure why you think such a particle would experience a field gradient as it moves (whether accelerating or otherwise) through a uniform magnetic field.

Well; I'm not sure either...that's why I asked the question...I guess I am thinking like my Engineering friends who always say: " If it can happen it will happen" LOL...and I'm not even sure it CAN happen.

However, I am probably speculating on possibilities based on what may be considered ancillary evidence from, for example. things like Aharonov-Bohm effect whereby a charge is passed through a Magnetic field-free region containing a Magnetic Vector potential and acquires a phase change...which I believe , if I'm not mistaken, deflects its trajectory.

So I extrapolate and think; "What would a magnetic dipole experience if it was accelerated through a field free region of Non-zero vector potential ?? Would its potential energy change? or acquire a phase change in its wave function? and what would be the effect?"

 

[Jilang]

Oh, I see what you are getting at. The distinction between a magnetic or an electric field is frame dependent.

 

[dante10]

Other than having orbital and spin angular momentum, the atom also has nuclear spin and hence the angular momentum associated with it. So, while carrying out the stern-gerlach experiment with say Rb, Ag or K; why doesn't the nuclear spin play a part in the deflection? Why is it not considered when carrying out the calculations for the deflection of the atoms on the detector?

 

[Nugatory]

why doesn't the nuclear spin play a part in the deflection? Why is it not considered when carrying out the calculations for the deflection of the atoms on the detector?

Its contribution is small enough to ignore; look at the first two posts of https://www.physicsforums.com/threads/stern-gerlach-and-nuclear-spin.805367/