# Electromagnetism: Direction of B-field

• Niles
In summary, Niles explains that if the z-component of the magnetic field points towards -z, the particle experiences a negative magnetic field. If the z-component of the magnetic field points towards +z, the particle experiences a positive magnetic 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 Bz points towards -z, then the particle experiences a negative magnetic field.

Is my resoning correct?Niles.

#### Attachments

• setup.PNG
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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

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?

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

Thanks, I understand.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.

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

ehild said:
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 mF=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 mF'=-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.

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

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.

## 1. What is the direction of the B-field in an electromagnet?

The direction of the B-field in an electromagnet is determined by the right-hand rule. If you point your thumb in the direction of the current flow, the direction of your fingers curled around the wire will indicate the direction of the B-field.

## 2. How does the direction of the B-field change in a solenoid?

In a solenoid, the B-field is directed along the axis of the solenoid. As you move from one end of the solenoid to the other, the direction of the B-field will alternate between pointing towards you and away from you.

## 3. Does the direction of the B-field change when the current changes?

Yes, the direction of the B-field is directly proportional to the current. As the current increases, the strength of the B-field increases and its direction remains the same. When the current decreases, the B-field weakens and its direction remains the same.

## 4. How is the direction of the B-field affected by the presence of a magnetic material?

The presence of a magnetic material can alter the direction of the B-field. In a ferromagnetic material, the B-field will be strengthened and directed along the material's magnetic domains. In a diamagnetic material, the B-field will be weakened and directed opposite to the external magnetic field.

## 5. Is the direction of the B-field the same as the direction of the magnetic force?

No, the direction of the B-field is not the same as the direction of the magnetic force. The magnetic force is perpendicular to both the direction of the B-field and the direction of the current. The direction of the magnetic force can be determined using the right-hand rule, where the thumb points in the direction of the current, the index finger points in the direction of the B-field, and the middle finger points in the direction of the magnetic force.

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