Steel ball bearing in a magnetic field

[piisexactly3]

I seem to be unable to confirm to myself what's really going here.

Basically, we have a rectangular shaped magnet with north and south at opposite ends. A steel ball bearing is placed to the left of the magnet where it is equidistant from the north and south ends. Consequently, a force pushes the ball to the centre of the magnet.

From my knowledge of Fleming's left hand rule and induction, a current needs to be present for forces to occur, however I do not see where the currents are. Is there a current in the magnet?

 

[Adithyan]

Do you know about Faraday's laws? If yes, then try applying his first law in this case.

 

[piisexactly3]

induced emf is covered in the syllabus but that's it.

 

[Adithyan]

Do you know WHAT is the cause for an induced current in a conductor?

 

[piisexactly3]

A change in magnetic field across a current right?

 

[Adithyan]

No. Change in magnetic flux induces an emf which produces an induced current. In the case you described in the question, the flux through the ball changes and hence produces an induced emf.

To understand this I think you should have a nice long read or watch some videos about Faraday's laws; this may be of help:



http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

Give some time to these and read more to understand the laws better; I am sure you will be able to solve this question after you do those. If you come across any difficulties, do let me know if I can help.

 

[piisexactly3]

Ok so it now seems that an induced current is caused by a change in magnetic field across a given charge not a current.

I think I have misinterpreted the original question in assuming that the ball bearing has been in the described position since the beginning of time. If that were the case, I see no reason for a change in magnetic field and therefore for an emf to be induced.

So am I correct in thinking that I should actually be assuming that the ball is being moved closer to the centre of the magnet thus causing a change in magnetic field?

 

[rude man]

I seem to be unable to confirm to myself what's really going here.

Basically, we have a rectangular shaped magnet with north and south at opposite ends. A steel ball bearing is placed to the left of the magnet where it is equidistant from the north and south ends. Consequently, a force pushes the ball to the centre of the magnet.

If you maintain the bearing in the middle as you describe, it will not be pushed towards the center of the magnet. A slight nudge away from the centerline in either direction (parallel to the magnet's moment vector) will pull it towards one of the poles.

Permanent magnets have what are called "Amperian currents" which are the result of electron spin at the edges of the magnet. So the magnet looks to the outside world much like a short excited solenoid.

 

[Adithyan]

Ok so it now seems that an induced current is caused by a change in magnetic field across a given charge not a current.

I think I have misinterpreted the original question in assuming that the ball bearing has been in the described position since the beginning of time. If that were the case, I see no reason for a change in magnetic field and therefore for an emf to be induced.

So am I correct in thinking that I should actually be assuming that the ball is being moved closer to the centre of the magnet thus causing a change in magnetic field?

The ball bearing hasn't been in the described position since the beginning of time. But you are wrong in assuming that the ball is being moved closer to the center. Rather, at time t=0, the ball bearing was taken from an infinite distance from the magnet to the described position within one step.

 

[rude man]

The ball bearing hasn't been in the described position since the beginning of time. But you are wrong in assuming that the ball is not being moved closer to the center. Rather, at time t=0, the ball bearing was taken from an infinite distance from the magnet to the described position within one step.

OK so it was moved to that position. The OP said ' Consequently, a force pushes the ball to the centre of the magnet. ' Did he/she mean 'subsequently' perhaps?

Still, there is no force on the bearing if it's placed on a line exactly half-way between the magnet's poles. It wants to go to one pole or the other.

 

[Adithyan]

OK so it was moved to that position. The OP said ' Consequently, a force pushes the ball to the centre of the magnet. ' Did he/she mean 'subsequently' perhaps?

Still, there is no force on the bearing if it's placed on a line exactly half-way between the magnet's poles. It wants to go to one pole or the other.

Sorry, had a typo in my last post, I meant ""you are wrong in assuming that the ball is being moved closer to the center"". I hope you understand.

There is a sudden change of magnetic flux through the ball which induces an emf and consequently the current and experiences a force as a consequence. So 'consequently' is the right word according to me.

 

[piisexactly3]

Thanks for the help so far. I have posted a link to the original question from an Olympiad paper, Q7, to remove ambiguity.
http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_AS_2009_QP.pdf

 

[Adithyan]

I now have begun to see that option B is correct one. The steel ball bearing will induce a current which turns it into a dipole. Since the dipole is placed in a magnetic field in the equatorial direction, it should move to the south pole of the bar magnet.

P.S : I didn't think of the direction of force until you posted the original question because the original post asked for an explanation of current induction.

 

[piisexactly3]

Ah here is the mark scheme http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_AS_2009_MS.pdf

 

[Adithyan]

The answer states

"A steel ball bearing would have N and S poles induced, so that it would be pulled in
both directions along a field line. However, the field is not uniform and the poles in
the denser part of the field would draw it further into the field , or the induced poles
are not diametrically opposite on the ball bearing. It would have a force directed
towards X.
"

According to Lenz's law, the ball should move towards an area where there is lesser magnetic flux crossing its cross section which apparently is at a direction away from the magnet.

 

[rude man]

The correct answer is C.

N and S poles are induced in the bearing in opposire direction to that of the magnet. So the magnet's N pole attracts the bearing's S pole and the magnet's S pole attracts the beraing's N pole. The net motion is thus towards X.

You can also use F = l(B ∇B)
B is magnitude of B and direction as shown on the diagram
∇B is towards the magnet at point X, i.e. perpendicular to B
l is the effective thickness of the bearing in the direction of ∇B.

So F points towards ∇B, i.e the point X.
Vectors in bold.

 

[Adithyan]

The correct answer is C.

N and S poles are induced in the bearing in opposire direction to that of the magnet. So the magnet's N pole attracts the bearing's S pole and the magnet's S pole attracts the beraing's N pole. The net motion is thus towards X.

You can also use F = l(B ∇B)
B is magnitude of B and direction as shown on the diagram
∇B is towards the magnet at point X, i.e. perpendicular to B
l is the effective thickness of the bearing in the direction of ∇B.

So F points towards ∇B, i.e the point X.
Vectors in bold.

But how can the N and S poles be induced in opp direction to that of magnet? According to Lenz's law it must induce the same orientation of poles.

 

[rude man]

But how can the N and S poles be induced in opp direction to that of magnet? According to Lenz's law it must induce the same orientation of poles.

The bearing gets magnetized such that its induced field opposes the external field. In your picture the external field goes from right to left (N to S due to the magnet). Therefore, the bearing must produce a field that opposes this direction. So its S pole must be to the right and its N pole must be to the left. That means that opposite poles face each other and attract each other, so the bearing as a whole moves towards the X point in the middle of the magnet.

We are dealing with ferromagnetism. Faraday's law is inapplicable here. There is no time rate of change of flux here at all. The induced currents in the bearing are not induced by a time rate of change of the magnetic field. Similarly, Lenz's law does not apply. In fact, the bearing wants to move towards the magnet and you'd have to apply a force in the opposite direction for it not to. This is in opposition to Lenz's law. Use faraday and Lenz only for non-magnetic media in an external magnetic field.

To get a physical feel for what's happening here you must think of the electrons in the bearing spinning about their axes. An external field applies a torque to each electron's magnetic moment which aligns the spin vectors to produce the opposing field. To fully understand the phenomenon requires quantum mechanics.

 

[Adithyan]

The bearing gets magnetized such that its induced field opposes the external field. In your picture the external field goes from right to left (N to S due to the magnet). Therefore, the bearing must produce a field that opposes this direction. So its S pole must be to the right and its N pole must be to the left. That means that opposite poles face each other and attract each other, so the bearing as a whole moves towards the X point in the middle of the magnet.

If S pole is to the right, then it simply leads to more magnetic field lines entering from right which contradicts your statement "the bearing must produce a field that opposes this direction".

We are dealing with ferromagnetism. Faraday's law is inapplicable here. There is no time rate of change of flux here at all. The induced currents in the bearing are not induced by a time rate of change of the magnetic field. Similarly, Lenz's law does not apply. In fact, the bearing wants to move towards the magnet and you'd have to apply a force in the opposite direction for it not to. This is in opposition to Lenz's law. Use faraday and Lenz only for non-magnetic media in an external magnetic field.

The ball is suddenly (in one step) introduced to a magnetic field, which results in a change of magnetic flux and hence it induces an emf. I see no reason why Faraday's laws are inapplicable. You yourself used Lenz's law in the first paragraph of your post.
Regarding ferromagnetism, I must mention that olympiad questions stick to electromagnetic induction and faraday's laws, they won't involve ferromagnetism in a problem.

 

[rude man]

If S pole is to the right, then it simply leads to more magnetic field lines entering from right which contradicts your statement "the bearing must produce a field that opposes this direction".



The ball is suddenly (in one step) introduced to a magnetic field, which results in a change of magnetic flux and hence it induces an emf. I see no reason why Faraday's laws are inapplicable. You yourself used Lenz's law in the first paragraph of your post.
Regarding ferromagnetism, I must mention that olympiad questions stick to electromagnetic induction and faraday's laws, they won't involve ferromagnetism in a problem.

I think you are misreading the question.
It says the bearing is placed at the indicated point. The force is applied after it is placed or it wouldn't move.

Furthermore, a 'steel ball bearing' is stated. Steel is very ferromagnetic.

I don't know what to say about the alleged olympiad content. Basically I have my doubts. I looked at the questions and they are very encompassing.

 

[rude man]

If S pole is to the right, then it simply leads to more magnetic field lines entering from right which contradicts your statement "the bearing must produce a field that opposes this direction".

No.
I know this looks confusing. The bearing field points S to N inside the bearing but it points N to S ouside the bearing. So the external field produced by the bearing opposes that of the bar. Draw some field lines to see.

It's like a battery in an electrical circuit. The current flows + to - outside the battery but - to + inside the battery.

The battery is a source of emf. The magnets (both of them) are sources of mmf (magnetomotive force). So the B fields point in opposite directions inside vs. outside.

 

[Adithyan]

Maybe I am misinterpreting the question. I think of reading more on ferromagnetism and then getting back to this question. Thank you for your replies. :)

 

[piisexactly3]

You can also find an explanation for the mutiple choice answers a few pages on in the mark scheme. It mentions how the field is non-uniform and so the ball bearing moves to where the density of the field is greater.

It's starting to make some sense as far as my limited knowledge allows me.