Did the particle deflect due to the change in B field to an E field in my frame?

[cragar]

Lets say I have a uniform line charge moving at a speed v. This will create the B field for our stern-gerlach experiment. Now I shoot neutrons or some other particle with spin that will be affected by the B field. Now let's say I am moving with this line charge at speed v. In my frame there is no B field just an E field. But I will still see the particle deflect based on its spin. Would i say the particle deflected in my frame because its B field is now and E field in my frame?

 

[mfb]

The Stern-Gerlach experiment needs a magnetic field which has a variable strength in the direction of the field lines. With your line charge, you get field lines around the wire, with the same strength along those lines. You do not a deflection in any system.

 

[cragar]

ok can we think of a setup where we could get deflection, and also put our selves in a frame where there is no B field. What about the B field of a moving charge or some other configuration.

 

[Vanadium 50]

You are making the assumption that one can invent such a frame. I think it's your responsibility to show such a frame exists, not the respondents'.

 

[Bill_K]

The neutron is deflected because of a force, namely the gradient of the B field acting on its magnetic dipole moment, F = (m·∇)B. Equivalently, there's term in the potential energy, V = m·B, and F is the gradient of V.

But when viewed from a moving frame in which B = 0, the Lorentz transformation has replaced the B field by an E field. Does that mean that V = 0 in this frame?

No! Because guess what happens to m? In the new frame, in which the neutron itself is moving, the magnetic dipole moment of the neutron is replaced by an electric dipole moment.

 

[cragar]

Ok thanks Bill K. the magnetic dipole moment is replaced by an electric dipole moment.
Thats what i thought. but mfb made it sound like it wasn't going to happen.