Deduction about Magnetic Poles surrounding a Conductor

[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.

 

[haruspex]

the magnetic field will point in the direction of the net electric field

Did you mean that?

Several things bother me about the question. I did wonder if it has been accurately worded in post #1, but at https://www.knowledgeboat.com/quest...wo-stretched-copper-wires--711181432220828700 I see exactly the same wording. I also see that the official-looking answer given there claims it does not matter which is which of the poles, merely that they be different. That's a stronger statement than in post #1, and seems extremely unlikely.

It also bothers me that we are not told the circuit is horizontal, that the F arrow looks like it is in the plane of the circuit, that it is shown as acting on the rod, and that it is not entirely clear whether the wording refers to the force on the rod or the force on the poles.

Finally, what is the significance of stretched wires versus a thick rod? It's the same current all the way around. Am I missing something?

 

[Delta2]

Did you mean that?

Several things bother me about the question. I did wonder if it has been accurately worded in post #1, but at https://www.knowledgeboat.com/quest...wo-stretched-copper-wires--711181432220828700 I see exactly the same wording. I also see that the official-looking answer given there claims it does not matter which is which of the poles, merely that they be different. That's a stronger statement than in post #1, and seems extremely unlikely.

It also bothers me that we are not told the circuit is horizontal, that the F arrow looks like it is in the plane of the circuit, that it is shown as acting on the rod, and that it is not entirely clear whether the wording refers to the force on the rod or the force on the poles.

Finally, what is the significance of stretched wires versus a thick rod? It's the same current all the way around. Am I missing something?

Yes the statement has issues but I think you are being a bit pedantic.

The core issue is that what is seems to be the official answer claims that the poles need just to be different which doesn't seem entirely correct to me.

 

[haruspex]

Yes the statement has issues but I think you are being a bit pedantic.

It is so sloppy I have no confidence that the question setter is adequately qualified.

 

[kuruman]

Did you mean that?

No, it was a typo that is now fixed. Thanks for the catch.

 

[kuruman]

First I will iterate that this is not a well-posed question. However, after some thought, I think I understand what it's about. An important clue is the passage "What should be the magnetic poles at points A and B lying on either side of the conductor $\dots$" Assuming that the author of the problem knows that magnetic monopoles do not exist, we have to consider that the aforementioned "poles" can be ends of bar magnets between which the conducting rod is placed. Note that the direction of the current in the rod is known and fixed.

There are two configurations of placing the rod between the "poles" around the rod, in attraction (figure below left) or in repulsion (figure below right). The direction of the current is out of the screen in both cases. The direction of the force on the rod (green arrow) can be found using the right hand rule. In each case I placed the rod in a region where the external magnetic field is mostly in one direction. Note that when the poles are in attraction, the force is perpendicular to the line joining A and B, but when they are in repulsion, the force is parallel to that line.

 

[Darshit Sharma]

Yes the statement has issues but I think you are being a bit pedantic.

The core issue is that what is seems to be the official answer claims that the poles need just to be different which doesn't seem entirely correct to me.

That is not an official answer tho. These websites just merely publish solutions to question papers which in most cases are wrong and misleading. Even some books too. I am so frustrated with all this. Even the SNOW and AMPERE SWIMMING RULE some webs and teachers use are just wrong.

Actually the council didn't publish an official board exam answer key last year. I will be appearing for the board exams in Feb.