# Can a magnetic field ever cause a translation motion?

In summary, according to the Lorentz Law, a charged particle moving with a velocity v in a magnetic field B will experience a force given by $\mathbf{F}=q\ (\mathbf{v} \times \mathbf{B})$
Lorentz Law says that for a charged particle moving with a velocity v in a magnetic field B then the force on it is given by $$\mathbf{F} = q (\mathbf{v} \times \mathbf{B})$$
Now, if I say that particle’s velocity and the magnetic field are aligned then according to Lorentz Law there will be no force on it and hence no attraction.
If we have something that have a magnetic moment $\mathbf{\mu}$ then the torque produced by magnetic field on it is $$\tau = \mathbf{\mu} \times \mathbf{B}$$
So, magnetic field seems to me to work only in rotational aspects and never causes any translational effect. I want to know if this is true.

Delta2
There can be a translational force on a magnetic moment given by ##\vec F=\nabla(\vec \mu \cdot \vec B)##

Can a magnetic field ever cause a translation motion?

What happens when a piece of iron gets near a magnet?

gmax137
I wonder where this thread will end up, thinking it might go towards the "is the magnetic field capable of doing work on matter?" way...

Dale said:
There can be a translational force on a magnetic moment given by ##\vec F=\nabla(\vec \mu \cdot \vec B)##
But why it is taught that magnetic dipole rotates in a field and never mentions that after being aligned it will move? I mean a side of dipole going to feel a force just equal and opposite to the other side, hence translational effect is not caused.

Delta2 said:
I wonder where this thread will end up, thinking it might go towards the "is the magnetic field capable of doing work on matter?" way...
I quite didn’t get you.

What happens when a piece of iron gets near a magnet?
That was the real problem and because of that I asked this question.

With a completely uniform magnetic field in a given direction, there are no forces along the direction of the field. However, from a magnetic pole, you always get some spreading of the field lines, which means besides a ## B_z ##, you get some finite ## B_x ## and/or ## B_y ##. This same question came up a year or two ago, but I don't have that post at my fingertips. I'll try doing a "search". Yes, I found it: See https://www.physicsforums.com/threa...elds-and-magnetic-moment.875780/#post-5500177

Last edited:
But why it is taught that magnetic dipole rotates in a field and never mentions that after being aligned it will move? I mean a side of dipole going to feel a force just equal and opposite to the other side, hence translational effect is not caused.
My class mentioned it. There is no translational force in a uniform B field. Perhaps your professor only got to cover uniform fields and ran out of time to cover non uniform fields in that lecture. You would have to ask the teacher why they didn’t cover it.

By the way, the magnetic moment doesn’t need to be aligned to have a force. It just can’t be perpendicular.

berkeman
I think I should express myself more clearly. Consider this image in attachment, in the image the red arrows represent the magnetic field B which is given by $\mathbf{B} = B_0 \hat i$ and in the blue square loop a current I is flowing and it's direction is mentioned by the arrows in each arm. The magnetic moment $\mathbf{\mu}$ is aligned with the field.
Now, by Laplace's equation force on each arm is $$\mathbf{F} = I\mathcal{l} \times \mathbf{B}$$
$$\mathbf{F_{AB}} = I (\mathbf{AB} \times \mathbf{B})$$
$$\mathbf{F_{AB}} = I~a~B_0 \hat j$$ we can assume that our loop is a square with all sides equal to a . Similarly, force on the arm CD is $$\mathbf{F_{CD}} = - I~a~B_0 \hat j$$
$$\mathbf{F_{AB}} + \mathbf{F_{CD}} = 0$$ which shows that there is no translational effect as the net force is force (we can do the similar calculations for the arms BC and AD) and the result would that $\mathbf{F_{net}} = 0$ which is the condition for translational equilibrium.
I request you all to please explain me through an analysis like this.

#### Attachments

• Screen Shot 2019-11-28 at 4.23.02 PM.png
12.8 KB · Views: 174
the magnetic field B which is given by ##B= B_0 \hat i##
Yes. Since the magnetic field is uniform ##\nabla(\vec \mu \cdot \vec B)=0##. If the field is not uniform then the forces on the different sides of the loop do not cancel out and there is a net translation force.

Last edited:
Dale said:
Yes. Since the magnetic field is uniform ##\nabla(\vec \mu \cdot \vec B)=0##. If the field is not uniform then the forces on the different sides of the loop do not cancel out and there is a net translation force.
Wow, I took a lot of time just understanding this thing. Thank you.
I just want to really thank you for replying me, if it would have been some other site or even my educational institute they would have given me everything (harsh remarks, this and that) except an answer like you did.
I’m really grateful to you.

berkeman, Ibix and Dale
No worries! I am glad I could help

## 1. Can a magnetic field cause an object to move?

Yes, a magnetic field can cause an object to move if the object has a magnetic property, such as being a magnet or containing magnetic materials.

## 2. How does a magnetic field cause motion?

A magnetic field causes motion by exerting a force on the magnetic materials within an object. This force is known as the Lorentz force and is dependent on the strength of the magnetic field and the velocity of the object.

## 3. Can any object be moved by a magnetic field?

No, only objects that have a magnetic property can be moved by a magnetic field. Objects that do not have a magnetic property will not be affected by a magnetic field.

## 4. What is the relationship between the strength of the magnetic field and the amount of motion it can cause?

The strength of the magnetic field is directly proportional to the amount of motion it can cause. This means that the stronger the magnetic field, the more force it will exert on an object and the greater the motion it can cause.

## 5. Can a magnetic field cause translation motion in a vacuum?

Yes, a magnetic field can cause translation motion in a vacuum. This is because the Lorentz force does not require a medium to act on an object, so it can still exert a force on an object in a vacuum.

• Electromagnetism
Replies
36
Views
3K
• Electromagnetism
Replies
1
Views
1K
• Electromagnetism
Replies
8
Views
822
• Electromagnetism
Replies
2
Views
764
• Electromagnetism
Replies
4
Views
993
• Electromagnetism
Replies
15
Views
3K
• Electromagnetism
Replies
5
Views
4K
• Electromagnetism
Replies
17
Views
2K
• Electromagnetism
Replies
1
Views
1K
• Electromagnetism
Replies
5
Views
670