Electromagnetism: Direction of B-field

[Niles]

Homework Statement

Hi

I have a current loop (see attached), and I have found the expression for the B-field along the axis of the loop. A particle moves through the loop, as also shown in the attached picture. Using the right hand, I let current run through the loop counter-clockwise, shown as well. My question is, what is the sign of the B-field that the particle experiences?

My own attempt is the following: So I know that the particle moves in the positive z-direction. Since the magnetic field B_z points towards -z, then the particle experiences a negative magnetic field.

Is my resoning correct?Niles.

 

[ehild]

Yes, If the particle travels along the axis of the ring and the current is counter-clockwise from the point of view of the particle, the direction of magnetic field is opposite to the direction of its velocity, points into the -z direction. The "negative magnetic field" is not a correct expression, as B is a 3D vector. If the particle does not travel along the z axis, the field it experiences is not parallel with z.

ehild

 

[Niles]

Thanks. But if I only confine my analysis to the axial direction (i.e. only z), then the particle must experience a negative B-field with the current setup?

 

[ehild]

There is no such thing as "negative B field". If the z axis points on the right, the z component of B is negative.

ehild

 

[Niles]

Thanks, I understand.Niles.

 

[Niles]

I'm actually not 100% sure I understand this after all. If the z-component of B points towards -z, will the magnetic field experienced by the atom be negative? By "negative magnetic field" I am referring to (for example) that the Zeeman shift $\propto m B$ for a magnetic substate m>0 will be negative.

 

[ehild]

When the Zeeman shift is derived the coordinate system is set up with z axis pointing in the direction of the magnetic field. The magnetic dipoles align with respect to the magnetic field. So "B" is positive in your formula.

ehild

 

[Niles]

When the Zeeman shift is derived the coordinate system is set up with z axis pointing in the direction of the magnetic field. The magnetic dipoles align with respect to the magnetic field. So "B" is positive in your formula.

ehild

Thanks for helping. There is something bothering me though: Say I have an atom in a state with zero magnetic quantum number m_F=0. Now I apply a magnetic field to it such that it is pointing towards +z. Now I turn on my laser with -hbar polarization, and make it point along +z, i.e. the atom is promoted to a state with m_F'=-1. In other words, the projection of F onto B yields -1*B. So far so good.

Now say that the direction of the magnetic field changes instantly fast by e.g. 120 degrees with respect to z. The atom will still be in the very same state, since it has no reason to change (i.e., no energy has been applied to it). However the spatial orientation must change.

Will the atom re-align itself such that the new projection of its magnetic moment onto (the new) B is -1*B?

Best wishes,
Niles.

 

[ehild]

I am not an expert on magnetic phenomena, so I might be wrong.
The magnetic momentum can be both positive and negative and also zero. It means how the atomic magnet is aligned with respect to the field. The energy of the atom depends on the alignment - can be higher or lower than the energy without the magnetic field. The atom can be excited to a higher energy state which means an other alignment.

If you change the direction of the magnetic field, the energy of the atomic magnets will change.

ehild

 

[Niles]

Thanks for that. I'll try and ask in the Quantum Physics subforum as well, but thanks for taking time to think/write about it.Niles.