Deduction about Magnetic Poles surrounding a Conductor

[Darshit Sharma]

Homework Statement

Magnetic poles at the points A and B lying on either side of the conductor to experience the force in the upward direction

Relevant Equations

Flemming's left hand rule and Right hand thumb rule

As shown in the diagram, a copper conductor is placed over two stretched copper wires whose ends are connected to a D.C. supply. What should be the magnetic poles at points A and B lying on either side of the conductor to experience the force in the upward direction?----------

----------
My understanding was that I tried to use Flemming's left-hand rule to figure out the polarity at the points. I followed the common manoeuvre which is as follows: I placed my central finger along the flow of current through the conductor and my thumb along the indicated force vector. A bit of confusion arose from here that the finger was just pointing from A to B so I used some of my understanding and concluded since the finger points towards B it may be as though the field lines were entering from below B and coming out of B i.e. perpendicular to the plane of the paper on which this dia is drawn. Since we see field lines coming out of that point I concluded that that point is the North pole and A is south.

Another thing was since the current flowed in a clockwise loop made with the conductor thus the pole at A must be south hence at B automatically north pole.

So after these two considerations, I concluded that the poles at A and B are the south and the north poles respectively.----------

This question was a test question in CISCE'S ICSE examination which we high schoolers give in India. (Grade 10).
However, the board didn't release an answer key this year.
And I had a cheap third-party answer booklet which just merely stated that the poles at A and B just need to be different not just specifically south and north.

Thus, the condensation is I wanted to ascertain whether my answer was right or not.

I want to understand the correct method by which the question can be solved, rather than my own pretty stupid method.

A better straightforward solution is anticipated.

Moreover, if anyone could instruct me where I lacked in the solution. Or if you notice any loopholes in my understanding.
(I ain't much confident though; I think I got this one wrong too)

Any help is appreciated.

 

[Delta2]

Hmm not sure if this matters for the final solution but does the full statement of the problem says if we can ignore the magnetic fields from the stretched copper wires?

 

[Darshit Sharma]

Hmm, not sure if this matters for the final solution but does the full statement of the problem say if we can ignore the magnetic fields from the stretched copper wires?

Nothing is mentioned about them but how will they have a magnetic field if they don't have current flowing through them even? I am kind of doubtful about the current flow too. It won't flow, right? So no current no magnetic field?

Edit: I was talking about the stretched copper wires past the conductor. Current won't flow in them, right? And for the wire that is included in the current loop made with the conductor. I don't think it will change the final answer. However, if it does we would have to consider it in our answer because nothing is explicitly told about them in the original question.

 

[Delta2]

Current will flow in the left portion of the circuit, because as far as I know copper wires whether thick or stretched are good conductors. That is the left segments (up left and down left )of the stretched copper wires will have equal and opposite currents.

The portions of the stretched copper wires that are after the thick copper conductor, in the right segment of the picture will not have current because the circuit is open.

I consider left and right segments relative to the thick copper conductor in the center.

 

[Delta2]

After some more careful thinking by me , I concluded that the magnetic fields from the stretched wires don't affect the solution and that your solution seems correct to me, that is A must be south pole and B must be north pole but not sure if your reasoning is 100% correct, let me read your post more carefully.

 

[Delta2]

I don't think you should use fleming's rule here but the right hand thumb rule.

https://en.wikipedia.org/wiki/Right-hand_grip_rule

 

[Darshit Sharma]

I don't think you should use fleming's rule here but the right hand thumb rule.

https://en.wikipedia.org/wiki/Right-hand_grip_rule

But how will we use the information about the Force that is given? right hand thumb rule just related current and magnetic field right? No info about the force?

 

[Delta2]

Ehm sorry I think I misunderstood the statement of the problem, do we want the force on the thick conductor to be upwards?

 

[Darshit Sharma]

Ehm sorry I think I misunderstood the statement of the problem, do we want the force on the thick conductor to be upwards?

Umm, Yeah

 

[Delta2]

Ok fine then indeed we have to use flemming left hand rule, but by doing so I concluded the A must be north and B south.

 

[Darshit Sharma]

Ok fine then indeed we have to use flemming left hand rule, but by doing so I concluded the A must be north and B south.

lol (I was just reading through your reply and was peacefully smiling until I saw some of your final words)

Could you please explain how? Why do our answers differ?

 

[Delta2]

Using FLHR I concluded that the field must point from A to B, hence A must be North and B south

 

[kuruman]

Using FLHR I concluded that the field must point from A to B, hence A must be North and B south

I agree with your conclusion.

 

[kuruman]

lol (I was just reading through your reply and was peacefully smiling until I saw some of your final words)

Could you please explain how? Why do our answers differ?

In what direction is the current, top to bottom or bottom to top in the figure?

Given the direction of the current, you know that the magnetic field must be perpendicular to the plane defined by the force and the current. Furthermore, the direction of the force is given by the vector cross product $\mathbf{F}=I\mathbf{L}\times\mathbf{B}$ where $\mathbf{L}$ is the length of the rod in the direction of the current. You need to find the direction of the field $\mathbf{B}$ that will give a force in the given direction using whatever-named rule you have learned to find the direction of a cross product.

 

[Delta2]

Homework Statement: Magnetic poles at the points A and B lying on either side of the conductor to experience the force in the upward direction
Relevant Equations: Flemming's left hand rule and Right hand thumb rule

A bit of confusion arose from here that the finger was just pointing from A to B so I used some of my understanding and concluded since the finger points towards B it may be as though the field lines were entering from below B and coming out of B i.e. perpendicular to the plane of the paper on which this dia is drawn. Since we see field lines coming out of that point I concluded that that point is the North pole and A is south.

Here lies the core of your reasoning. It is completely correct when you say that the (first) finger (the pointer finger, not the thumb finger) is pointing from A to B, hence that is the desired direction of the magnetic field. It is well known fact that the magnetic field points from North to South. I can't follow the rest of your reasoning that says that magnetic field lines entering from below B and coming out of B. You do some sort of intuitive thinking in 3D space which i cant follow but thinking in 3D (regarding the magnetic field lines, of course we have to think in 3D regarding the FLHR) is not required here, once we know the direction of the magnetic field as an arrow pointing from A to B, that is all that we need.

 

[Darshit Sharma]

Using FLHR I concluded that the field must point from A to B, hence A must be North and B south

Ohhkk I don't know why I was so confused while making the final judgement.

One more question: If we were not told about the force that is if it were just a simple loop then what would be the magnetic field at A ? South?

 

[Darshit Sharma]

Here lies the core of your reasoning. It is completely correct when you say that the (first) finger (the pointer finger, not the thumb finger) is pointing from A to B, hence that is the desired direction of the magnetic field. It is well known fact that the magnetic field points from North to South. I can't follow the rest of your reasoning that says that magnetic field lines entering from below B and coming out of B. You do some sort of intuitive thinking in 3D space which i cant follow but thinking in 3D (regarding the magnetic field lines, of course we have to think in 3D regarding the FLHR) is not required here, once we know the direction of the magnetic field as an arrow pointing from A to B, that is all that we need.

Ohk ohk Thanks sir! "My intuitive thinking" lol I am fully satisfied by the answer but why dont we have to think in 3d?

 

[Delta2]

Ohhkk I don't know why I was so confused while making the final judgement.

One more question: If we were not told about the force that is if it were just a simple loop then what would be the magnetic field at A ? South?

The magnetic field at the point A, from the current at the thick conductor has direction from above the plane of page to below the plane of page. Using the right hand thumb rule i got that conclusion.

Ohk ohk Thanks sir! "My intuitive thinking" lol I am fully satisfied by the answer but why dont we have to think in 3d?

Ehm if I understand well you imagine that we have some sort of bar magnet placed in the line between from A to B and you imagine the magnetic field lines in 3D space from this bar magnet. You don't have to think like this for this problem. All you need is that the magnetic field must point from A to B, so if we have a (hypothetic) magnetic North monopole at A and a magnetic South monopole at B the produced magnetic field will point from A to B, pretty much like if we have a positive charge at point A and a negative charge at point B the Electric field would point from A to B.

 

[Darshit Sharma]

The magnetic field at the point A, from the current at the thick conductor has direction from above the plane of page to below the plane of page. Using the right hand thumb rule i got that conclusion.

Ehm if I understand well you imagine that we have some sort of bar magnet placed in the line between from A to B and you imagine the magnetic field lines in 3D space from this bar magnet. You don't have to think like this for this problem. All you need is that the magnetic field must point from A to B, so if we have a (hypothetic) magnetic North monopole at A and a magnetic South monopole at B the produced magnetic field will point from A to B, pretty much like if we have a positive charge at point A and a negative charge at point B the Electric field would point from A to B.

Ok for that 3d reasonings

So what is your final verdict for the pole at A? South?

 

[Delta2]

So what is your final verdict for north pole at A? South?

we should have a north pole above point A and a south pole below point A so that the magnetic field produced by these poles point from above the plane of page to below the plane of page.

A (hypothetic) magnetic monopole placed at point A cant produce the same magnetic field as that of the thick conductor regardless if it south or north monopole.

 

[Darshit Sharma]

we should have a north pole above point A and a south pole below point A so that the magnetic field produced by these poles point from above the plane of page to below the plane of page.

A (hypothetic) magnetic monopole placed at point A cant produce the same magnetic field as that of the thick conductor regardless if it south or north monopole.

Whttt? I don't know why things aren't making any sense

Do you know about clock rule Sir? https://byjus.com/question-answer/s...etermining-the-polarities-of-a-circular-wire/That provides a South for the top
and because if we look from below the page we would obv see the current flowing in anti clock direction which means that it would be North down there

 

[Delta2]

Yes ok , the link explains it correct, seems once again I misunderstood your question, I thought you were asking what is the magnetic field at A produced by the thick copper conductor at the diagram of original post.

 

[Darshit Sharma]

Yes ok , the link explains it correct, seems once again I misunderstood your question, I thought you were asking what is the magnetic field at A produced by the thick copper conductor at the diagram of original post.

I was feeling like your explaination was corrrect because the right hand thumb rule's fingers point from above and outside the paper to inside the paper and below and as you said it could only be possible if there was a north pole above the loop. So it should be north pole na. Then why does the clock rule says south ?

 

[Darshit Sharma]

Yes ok , the link explains it correct, seems once again I misunderstood your question, I thought you were asking what is the magnetic field at A produced by the thick copper conductor at the diagram of original post.

I understood about the conductor problem now we are just talking about the normal plain copper loop with just a battery.

And the clockrule doesn't works for the conductor froblem because there is the direction of force given explictly right?

 

[Delta2]

I understood about the conductor problem now we are just talking about the normal plain copper loop with just a battery.

And the clockrule doesn't works for the conductor froblem because there is the direction of force given explictly right?

To find the direction of magnetic field produced by a current distribution you can use various rules.

But to find the direction of the "BIL" force , given the magnetic field(that is produced by some other external source) and the current distribution is another set of rules.

 

[Delta2]

I was feeling like your explaination was corrrect because the right hand thumb rule's fingers point from above and outside the paper to inside the paper and below and as you said it could only be possible if there was a north pole above the loop. So it should be north pole na. Then why does the clock rule says south ?

I am not sure I understand you anymore, From what I can understand you are confusing the magnetic field produced by a current distribution, with the external magnetic field that must be present so that the BIL force on the current distribution must be what it is.

 

[Darshit Sharma]

To find the direction of magnetic field produced by a current distribution you can use various rules.

But to find the direction of the "BIL" force , given the magnetic field(that is produced by some other external source) and the current distribution is another set of rules.

For the BIL force we used FLHR
ok?

Now for the current distribution we are using - Right hand thumb rule and the clock face rule
right?

So now for the current distribution problem - what is the polarity at A when looked from above?

 

[Delta2]

So now for the current distribution problem - what is the polarity at A when looked from above?

What is the current distribution, a rectangular loop or a circular loop cause the link you provided is for circular loops.

To be honest I don't understand a question asking for polarity of magnetic field at a point

 

[Darshit Sharma]

What is the current distribution, a rectangular loop or a circular loop cause the link you provided is for circular loops.

To be honest I don't understand a question asking for polarity of magnetic field at a point

it should be the same in case of a rectangular loop also, right?The question is in plain terms: If there was no force arrow in the question and there was just a simple normal loop of wire and conductor - then what would be the polarity at point A when looked from above?

 

[Delta2]

it should be the same in case of a rectangular loop also, right?The question is in plain terms: If there was no force arrow in the question and there was just a simple normal loop of wire and conductor - then what would be the polarity at point A when looked from above?

Sorry I went to eat something, yes it should probably be the same for rectangular loop as well.

BUT my problem remains, I don't quite understand the question what is the polarity of the magnetic field at a point. What is the direction of the magnetic field at a point, yes it is a proper question but what is the polarity I just don't feel the question. Maybe @kuruman could help here.

 

[Darshit Sharma]

Sorry I went to eat something, yes it should probably be the same for rectangular loop as well.

BUT my problem remains, I don't quite understand the question what is the polarity of the magnetic field at a point. What is the direction of the magnetic field at a point, yes it is a proper question but what is the polarity I just don't feel the question. Maybe @kuruman could help here.

No worries
Maybe I should draw a new neat figure for the second question by hand. I'll do it in some time for sure.

 

[kuruman]

Maybe @kuruman could help here.

It is not a well-phrased question. Here is my interpretation and my reasoning for it.

We have two rails connected to a power supply and a rod across the rails completing the circuit. A current runs through the rod and the rod experiences a Lorentz force perpendicular to the plane of the rails due to the presence of an external magnetic field. In most, if not all, problems with this kind of setup the magnetic field is uniform and we can assume it to be so here.

The question that, I think, is really asked is "What direction must this external magnetic field have so that the force is perpendicular to the rails as shown?" Thus, after we answer the real question, we have to figure out which pole of the magnet creating the external field should go to A and which to B.

 

[Darshit Sharma]

It is not a well-phrased question. Here is my interpretation and my reasoning for it.

We have two rails connected to a power supply and a rod across the rails completing the circuit. A current runs through the rod and the rod experiences a Lorentz force perpendicular to the plane of the rails due to the presence of an external magnetic field. In most, if not all, problems with this kind of setup the magnetic field is uniform and we can assume it to be so here.

The question that, I think, is really asked is "What direction must this external magnetic field have so that the force is perpendicular to the rails as shown?" Thus, after we answer the real question, we have to figure out which pole of the magnet creating the external field should go to A and which to B.

Yes

Till now what I have understood and @Delta2 has made me understand is that the field is directed from A to B which implies that the pole at A should be a North monopole and at B a South monopole. This was well endorsed by you in #13. However, while approving all these things and clearing my doubts after @Delta2 said the following:

To find the direction of the magnetic field produced by a current distribution you can use various rules.

But to find the direction of the "BIL" force, given the magnetic field(that is produced by some other external source) and the current distribution is another set of rules.

I simultaneously, to get a deeper insight into this topic, raised another question which was separate from the already-in-discussion question. The question was: If there was no force arrow given in the original question i.e. just a simple square loop of wire involving a conductor in its path was given then what would be the magnetic pole at point A?

@Delta2 was right when he said I was confusing both of these things.

I am not sure I understand you anymore, From what I can understand you are confusing the magnetic field produced by a current distribution, with the external magnetic field that must be present so that the BIL force on the current distribution must be what it is.

Moreover, while reading the conversation myself I discovered that I was not clear throughout and I am solemnly conscience-stricken.

Therefore, the new and final question is:

If I have a square loop of wire as shown in the figure below, what will be the direction of the magnetic field and thus, the polarity inside the loop when viewed from above that is as we are viewing the screen.

My try at this:

If I try to use the "Right hand thumb rule" and place my thumb along the current I2, I get a grip something like this which I have tried explaining:
My fingers curl inward from within the plane outside the loop (To the left of AB) then curl over AB and finally curl into the square loop. Now, as @kuruman explained to me in another post if I imagine a tangent at that point (which point? The point at which my curling fingers pierce through the plane, inside the square loop) the tangent obviously points below the plane ABCD now as I'm told by @Delta2 that if I have a field which is directed from above the plane then into it and then finally below it, I'll get a north monopole above the plane ABCD and a south monopole below the plane ABCD because the field lines must be going from the north to the south.

Thus, after solving the preliminary question, My first question is in which direction will the compass needle point if it is placed inside the loop? How could it point inside the plane (or paper whatever)?

Second, if I place the needle above the wire AB, the north is at the inside of the loop, right? then why does the needle point towards the left that is to the left of the wire whereas it should have done toward the right (i.e. towards the middle of the loop where the north is)?

 

[Delta2]

I don't know the exact magnetic field lines produced by a square loop current distribution. My guess is that it will be similar to a circular current loop. At the center of the square loop and given the current direction given as clockwise the magnetic field will point towards below the plane of page.

 

[kuruman]

Yes

Till now what I have understood and @Delta2 has made me understand is that the field is directed from A to B which implies that the pole at A should be a North monopole and at B a South monopole. This was well endorsed by you in #13. However, while approving all these things and clearing my doubts after @Delta2 said the following:

I simultaneously, to get a deeper insight into this topic, raised another question which was separate from the already-in-discussion question. The question was: If there was no force arrow given in the original question i.e. just a simple square loop of wire involving a conductor in its path was given then what would be the magnetic pole at point A?

@Delta2 was right when he said I was confusing both of these things.Moreover, while reading the conversation myself I discovered that I was not clear throughout and I am solemnly conscience-stricken.

Therefore, the new and final question is:

If I have a square loop of wire as shown in the figure below, what will be the direction of the magnetic field and thus, the polarity inside the loop when viewed from above that is as we are viewing the screen.
View attachment 338624

My try at this:

If I try to use the "Right hand thumb rule" and place my thumb along the current I2, I get a grip something like this which I have tried explaining:
My fingers curl inward from within the plane outside the loop (To the left of AB) then curl over AB and finally curl into the square loop. Now, as @kuruman explained to me in another post if I imagine a tangent at that point (which point? The point at which my curling fingers pierce through the plane, inside the square loop) the tangent obviously points below the plane ABCD now as I'm told by @Delta2 that if I have a field which is directed from above the plane then into it and then finally below it, I'll get a north monopole above the plane ABCD and a south monopole below the plane ABCD because the field lines must be going from the north to the south.

Thus, after solving the preliminary question, My first question is in which direction will the compass needle point if it is placed inside the loop? How could it point inside the plane (or paper whatever)?

Second, if I place the needle above the wire AB, the north is at the inside of the loop, right? then why does the needle point towards the left that is to the left of the wire whereas it should have done toward the right (i.e. towards the middle of the loop where the north is)?

You have to understand that at any point in space the magnetic field will point in the direction of the net electric magnetic field which is the sum of the contributions from all nearby electric currents, i.e. all parts of the loop. One more time, the direction of this net magnetic field and hence the orientation of the magnetic needle depends on where you place the needle.

It is worth pointing out that a current loop has a magnetic dipole moment. Its magnitude is $\mu = IA$ where $I$ is the current in the loop and $A$ is its area. The direction of this magnetic dipole is given by the right hand rule: Curl the fingers of your right hand to match the circulating current and the direction of the magnetic dipole is perpendicular to the plane of the loop in the direction of your thumb. The figure on the right shows the magnetic field lines generated by a circular current loop. I could not find a picture for a square loop but it's going to be very similar. Try to imagine the direction of a compass needle placed at different points in the space around the loop.