# A confused Compass Needle between two solenoids

• Darshit Sharma
Darshit Sharma
Homework Statement
If a small magnetic compass needle was placed at point Z, what direction would its north pole point?
Relevant Equations
Flemming's Left hand rule. Clock Rule. Right Hand thumb rule
Original Question: If a small magnetic compass needle was placed at point Z, what direction would its north pole point? Explain your answer

My try:

Since the current flowed in an anticlockwise loop in the first wire => North pole was formed inside the loop => Outside the wire near the point Z it should be the South pole.

Since the current flowed in an clockwise loop in the second wire => South pole was formed inside the loop => Outside the wire near the point Z it should be the North pole.

So now? How to proceed further?Moreover I have a foreboding that I am just thinking of the question as there were simply two loops of wire but it would be diffect just beacuse to the solenoids. Thus I request you guide me first ignoring the solenoids like where will the compass needle point in just the case of two simple loops ? Then afterwards we may discuss the case of solenoids.

There is no difference between simple loops and solenoids to the method used for the answer. The method is (a) Find the direction of the net magnetic field at point Z and (B) Decide the direction in which the needle will align itself. For this part you will need to understand how a compass needle works.

kuruman said:
There is no difference between simple loops and solenoids to the method used for the answer. The method is (a) Find the direction of the net magnetic field at point Z and (B) Decide the direction in which the needle will align itself. For this part you will need to understand how a compass needle works.
The net field at Z is zero right? So compass is free to rest in Earth's Magnetic North - South direction?

Darshit Sharma said:
The net field at Z is zero right? So compass is free to rest in Earth's Magnetic North - South direction?
Why is the net field zero? Note that point Z is not on the common axis of the solenoids. Sketch some magnetic field lines from each solenoid noting that they form closed loops. How do they add at point Z?

kuruman said:
Why is the net field zero? Note that point Z is not on the common axis of the solenoids. Sketch some magnetic field lines from each solenoid noting that they form closed loops. How do they add at point Z?
But the magnetic field caused due to those two separate strands of wires of both the loops is zero, right?
And Sir, I am not able to make the field lines for the solenoids using the FLHR. Can you illustrate how?

Darshit Sharma said:
But the magnetic field caused due to those two separate strands of wires of both the loops is zero, right?
Why?
Darshit Sharma said:
And Sir, I am not able to make the field lines for the solenoids using the FLHR. Can you illustrate how?
Search the internet. What should you search for if you don't know what magnetic field lines due to a solenoid look like?

kuruman said:
Why?

Search the internet. What should you search for if you don't know what magnetic field lines due to a solenoid look like?
This is what I could draw

I am not able to judge the final net fild and direction at that point and moreover I doubt about the polarities about my solenoids.and about those straight wires - Using right hand thumb rule both cancel out naOr you could use the clock rule
Since the current flowed in an anticlockwise loop in the first wire => North pole was formed inside the loop => Outside the wire near the point Z it should be the South pole.

Since the current flowed in an clockwise loop in the second wire => South pole was formed inside the loop => Outside the wire near the point Z it should be the North pole.

First of all you ignore the straight wires because they produce a negligible magnetic field at point Z. The polarities of your solenoids are fine. Shown on the right is a clearer picture from what you have. If you place a magnetic needle at point Z, in what direction do you think its N-S line will be? Your choices are
1. To the left.
2. To the right.
3. From bottom to top.
4. From top to bottom.
5. Out of the plane of the screen.
6. Into the plane of the screen.

4 From top to bottom

I think so because the blue arrows are tangent to magnetic field lines which tells us the direction of magnetic field i.e. the North will be at the head of the arrow.

Since we have them going to both sides I think the needle will wobble a bit left-right-left-right then finally come to rest in North - top and South - Bottom positionbut there is a whole new doubt now
in this picture since the pre-drawn (printed) black colour field lines are going towards the south pole this means that the south poles are at both the terminal ends of the magnets this means the needle's south pole (shown in maroon by mistake which should be the black or grey (non-red) end that points towards south) would point towards the top that means this time North for the needle will be at bottom instead of top

Condensation - his time the south tip of the needle will point towards the top as shown in the figure with maroon and the north tip will point towards the bottom

So option 3)

which reasoning is correct? And now I feel that I am even doubtful of that tangent thing - if we draw a tangent at a point on the magnetic field line like I did in blue in the previous pic then the arrow will point towards the South or North?

In post #2 I gave a link that has a figure showing a compass needle in the earth's magnetic field. Study this figure. What conclusion can you draw about how magnetic needles line up in an external magnetic field? Forget which pole is where. All you have to do is figure out the direction of the net magnetic field at point Z.

kuruman said:
In post #2 I gave a link that has a figure showing a compass needle in the earth's magnetic field. Study this figure. What conclusion can you draw about how magnetic needles line up in an external magnetic field? Forget which pole is where. All you have to do is figure out the direction of the net magnetic field at point Z.

4) From top to bottom
I mean North points towards top

An additional and slight request: Can you tell me do both these statements convey the same thing?
Statements: "N-S line is From top to bottom" and "North points towards top and south points towards bottom"

Darshit Sharma said:

4) From top to bottom
I mean North points towards top

An additional and slight request: Can you tell me do both these statements convey the same thing?
Statements: "N-S line is From top to bottom" and "North points towards top and south points towards bottom"
Is this correct? And why does that South Poles thing not work?

Choice 3 is correct. The best way to think about it is this. A magnetized compass needle has a magnetic moment vector associated with it. This vector can be represented as an arrow with its tail at the south pole of the needle and its tip at the north pole of the needle. When placed in an external magnetic field, the needle will experience a torque that will turn it so that its magnetic moment is in the same direction as the local external magnetic field. This is a restoring torques which means that the needle may oscillate about its equilibrium position a few time before its energy is dissipated by friction and air resistance.

The take home message is that magnetic needles line up with their magnetic moment parallel to the external magnetic field.

kuruman said:
The take home message is that magnetic needles line up with their magnetic moment parallel to the external magnetic field.
If the magnetic field is from X to Y, then:
i) the magnetic moment will be X to Y, right?
ii) The arrow of the vector will points towards Y?

Darshit Sharma said:
If the magnetic field is from X to Y, then:
i) the magnetic moment will be X to Y, right?
ii) The arrow of the vector will points towards Y?
You are asking the wrong question. Look at the figure below. It shows magnetic field lines (black arrows) and the magnetic moment of a compass needle (red arrow). Note that
There is only one field line that points from X to Y. You cannot say that the magnetic field is from X to Y.
The magnetic moment is parallel to all the magnetic field lines.
The magnetic moment does not point towards Y. If it did, it would not be parallel to the field lines.

Darshit Sharma
kuruman said:
The take-home message is that magnetic needles line up with their magnetic moment parallel to the external magnetic field.
Isn't it like this: For choice 3 to be correct the compass needle needs to point towards the south?

Because the tangents on the lines near point Z point in the direction of the magnetic field. Now magnetic needle will point in the direction of the magnetic field as per your statement about this torque thing.

This implies that if 3rd choice that is bottom to top is correct then the pole laterally above Z would be south. This would mean that the magnetic needle points toward the south. Huh?

How? Wait what? In this image, the needles are pointing towards the south. Huh? Why? and when it is the south pole in the picture then why it is written in red that it is the magnetic north pole? South pole? North pole? both?

I think that you now understand magnetic moments. The magnetic moment of the compass needle is from the black (S) end to the red (N) end. Look at the picture. The magnetic moment is always in the same direction as the local Earth's field. You can also see that the Earth's North geographic pole is very near the Earth's South magnetic pole and vice versa for the other side. That's a point that people don't always realize or understand.

kuruman said:
You are asking the wrong question. Look at the figure below. It shows magnetic field lines (black arrows) and the magnetic moment of a compass needle (red arrow). Note that
There is only one field line that points from X to Y. You cannot say that the magnetic field is from X to Y.
The magnetic moment is parallel to all the magnetic field lines.
The magnetic moment does not point towards Y. If it did, it would not be parallel to the field lines.

View attachment 338627
Understood, Sir!Doubt:
Can't be there curved magnetic field lines from X to Y?
In that case, the red arrow will be the tangent to any one of the field lines (pointing towards Y) or the red arrow will be parallel to all of those lines?

The needle rests in the direction of the tangent to the field line, right? So if X and Y were magnetic dipoles with X being the North and Y being the South then we would get curved lines right? so then the red arrow will also be curved or it will be the tangent to any of those one curved lines?

And as you said the needle rests in the direction of the magnetic moment, the moment should point towards Y? just in case of dipoles.

Darshit Sharma said:
The needle rests in the direction of the tangent to the field line, right? So if X and Y were magnetic dipoles with X being the North and Y being the South then we would get curved lines right? so then the red arrow will also be curved or it will be the tangent to any of those one curved lines?
The word "dipole" means two poles, North and South taken together as a unit. You cannot have X and Y as magnetic dipoles. You can have one dipole (small magnet) at X and another one like it at Y. Or you can have one long bar magnet with one pole at X and the other at Y.

In any case, if you have a curved magnetic line from X to Y, the needle will be tangent to the local field line at where its midpoint is. You should also consider that the curvature of the field lines is usually much larger than the length of a compass needle so that you can easily take the field to be a straight line over the length of the needle. If the needle shown in the picture in post #16 were drawn to scale, it would be the size of the width of the Arabian peninsula, about 1,000 miles.

kuruman said:
You can also see that the Earth's North geographic pole is very near the Earth's South magnetic pole and vice versa for the other side. That's a point that people don't always realize or understand.
I can't believe my eyes. However, why it is written that it is Earth's North magnetic pole whereas the bar magnet depiction says that it should be Earth's South magnetic pole?

Sir, I am really mesmerized by your and @Delta2's knowledge and the will to help me despite my vague questions. However, it's 1 a.m. local IST in India currently and I do have my History exam tomorrow at 8 O'clock so I must take pains to see that unpleasant book. I'll connect to you shortly.
Thank you.

kuruman said:
The word "dipole" means two poles, North and South taken together as a unit. You cannot have X and Y as magnetic dipoles. You can have one dipole (small magnet) at X and another one like it at Y. Or you can have one long bar magnet with one pole at X and the other at Y.

In any case, if you have a curved magnetic line from X to Y, the needle will be tangent to the local field line at where its midpoint is. You should also consider that the curvature of the field lines is usually much larger than the length of a compass needle so that you can easily take the field to be a straight line over the length of the needle. If the needle shown in the picture in post #16 were drawn to scale, it would be the size of the width of the Arabian peninsula, about 1,000 miles.
Thank you once again for clearing my misconception; this time regarding dipole.

Now if XY were to be a bar magnet.
Just a simple bar magnet and I know nothing about it nor do you know anything about it.
So if the magnet is kept on a table and I place a magnetic needle near it and the needle points towards X.
What inference can I draw? X is the south pole of the bar magnet.

By using the word "points" I mean the red tip points.

From childhood, we heard that the needle points towards "the north pole", By looking at the image I learned that the needle points towards "the south pole".
Good Heavens! Oh! we colloquially say it points "towards north" means it points towards geographic north but the physics behind it is that the needle points towards the magnetic south which is near the geographic north.
Done! Clear!

Now let's see if the same applies to the bar magnet or not. If my permutations and combinations are correct, X should be the magnetic south of the bar magnet.

Darshit Sharma said:
I can't believe my eyes. However, why it is written that it is Earth's North magnetic pole whereas the bar magnet depiction says that it should be Earth's South magnetic pole?
What it says is correct. I hope I am not adding to the confusion. Here is the complete picture.
The North geographic pole has to do with the Earth's rotation. It is the point where the Earth's axis of rotation intersects the Earth's surface.
The North geomagnetic pole is near but not at the North geographic pole. However, as you can see in the figure, if you were to pretend that the Earth's magnetic field is generated by a gigantic bar magnet with a North and South pole, the South pole of this magnet would be the North geomagnetic pole. I know all this sounds confusing. In post #17 I was referring to the model of the Earth's magnetic field as that of a bar magnet.

If you are interested, this Wikipedia article sorts it all out in more detail than I can provide here.

kuruman said:
I know all this sounds confusing. In post #17 I was referring to the model of the Earth's magnetic field as that of a bar magnet.
Indeed, it was confusing. It's hilarious to have three poles but all this is sorted up now and all the praise goes into your hands, Sir. I now have a Wikipedia article to read at my leisure. Everything is cleaned up finally.

Now just that Bar Magnet thing is left at last. No sooner will I hear from your mouth, "Yes the needle will point towards the bar magnet's south pole" than I'll be full of the joys of spring and jump in ecstasy off my bed.

Darshit Sharma said:
Now just that Bar Magnet thing is left at last. No sooner will I hear from your mouth, "Yes the needle will point towards the bar magnet's south pole" than I'll be full of the joys of spring and jump in ecstasy off my bed.
Alas, you will not hear that from my mouth. You asked
Darshit Sharma said:
So if the magnet is kept on a table and I place a magnetic needle near it and the needle points towards X.
What inference can I draw? X is the south pole of the bar magnet.
The answer is "It depends on where you place the magnetic needle." Look again at the drawing of the Earth and the magnetic needle. Follow along a field line from one magnetic pole of the Earth to the other. Does the needle point always towards the gigantic bar magnet's south pole? I don't think so.

I wish you good luck on your History exam tomorrow. I will sign off for now.

Darshit Sharma
kuruman said:
I wish you good luck on your History exam tomorrow. I will sign off for now.
Sure, Sir.

The confusing thing about the labeling of North and South is that the labeling started 100's of years ago. At the time no one knew about the Earths magnetism. All they knew was that some rocks (magnetite), when suspended, would point in a given direction.

Since this was likely discovered in the Northern hemisphere, and there was some awarness (eventually) of there being a geographic North pole, these special stones were labeled so that the end that pointed North was called the North Pole of The Stone.

Much later in time people realized that the reason for this was something they named Magnetism. Of course this was intensly looked in to.

To this day we still label the compass needle so that the end that points to the geographic North is labeled the geographic North magnetic pole. (Which of course means that the Earths South magnetic pole is near the geographic North pole!)

(sorry, no references for that. it is just a 'factoid' that i collected over the years.)

[EDIT]
Well, it seems that the "factoid" I collected may have been wrong.
See this video:

Cheers,
Tom

Last edited:
hutchphd, Darshit Sharma and Delta2
kuruman said:
Alas, you will not hear that from my mouth. You asked

The answer is "It depends on where you place the magnetic needle." Look again at the drawing of the Earth and the magnetic needle. Follow along a field line from one magnetic pole of the Earth to the other. Does the needle always point towards the gigantic bar magnet's south pole? I don't think so.

I wish you good luck on your History exam tomorrow. I will sign off for now.
Sir, could you please provide me with a visual example where the needle will, in one case, point towards the south and, in another case, towards the north pole (depending upon its placement)?Before all our discussions, I used to think that the needle would always point towards the north of a bar magnet (not Earth's but just a simple one lying on the table) and the location or the direction of the North pole may change as per the placement of the magnetic needle. I doubt that I am mistaken.

However, there's another question:

Now, I find myself sufficiently adept to answer subpart (ii). However, I am still confused about (i) and (iii). I know you are trying to make me understand but I am unable to relate to it; I don't know why it is so.I have heard about the "AMPERE SWIMMING RULE" which used to say something like if you imagine yourself swimming along the current such that the current enters from your feet and leaves from your head then your left hand gives the direction of the magnetic field at that point.
but that used to be the case when the needle was above the wire and here the needle is below the wire, so technically what I have learnt till now, is that the direction the needle's pointing should be reversed, i.e. if according to the image, first, it should be towards the East if the needle is above the wire but since for the (i) the needle is below the wire, it should then point towards my right, i.e. towards the West.
So according to this "SNOW rule" and "AMPERE SWIMMING RULE" I concluded the following:
(I) West (ii) EastOnce again, as always, I was wrong in my reasoning, and the answer key says just the opposite (I) East (ii) WestI don't know where I went wrong, I tried to use the Right hand thumb rule but was unable to do so because I was confused whether to imagine the needle below in 3-D or in 2-D as @Delta2 told me that we have to think in 2D but if we think 2-D then the direction of the magnetic field do come vertically below the needle. How could the needle point that way?

Confused :(

Darshit Sharma said:
Confused :(
Anyway, I didn't give up this time. I tried again. thought it off as 3D. Unfortunately, the next few words are some of the words that manifest my perplexed state of mind.

In my first post about that conductor thing, Sir you and @Delta2 told me the following:
kuruman said:
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.

Both of you agreed that since the magnetic field( or field line or lines) is/are from A to B, the pole at A should be a North pole and the pole at B a South pole. Yes? I understood correctly, didn't I?
Ok so the thing that made A north pole was that the field lines were coming from A and the thing that made B south pole was that the field lines were going towards B. According to my basic mediocre knowledge, since we are not inside some bar magnet, it is obvious that the lines might be coming from a North pole and going towards south pole. That's how we concluded my first question.

But as I learned from a recent thread of @kuruman the north for field lines due to a current carrying wire also vary as we move along our curl of finger.

So I tried that thing and after thinking of the setup as the needle below the wire (in a 3D plane) I noticed that the tangent to curl of my fingers at the needle was directed towards the East.

So now we have the following choices:
1) If we assume the tangent to curl of my fingers as an arrow, the arrow points towards the North ( the geographic East), which would imply that the answer to my first question was wrong as in that case, the arrow pointed towards the South. (Remember A to B flow........A north....B south)

2) The needle of the compass points towards the south. So if we choose this assumption then your answer to my first question stands valid as the now If we assume the tangent to curl of my fingers as an arrow, the arrow points towards the South this time ( the geographic East) and so do the needle.

I am so confused :(
I request that you try just once simply answering the question in the pic and then explaining to me using a picture simultaneously explaining the difference with the first question.

Darshit Sharma said:
Sir, could you please provide me with a visual example where the needle will, in one case, point towards the south and, in another case, towards the north pole (depending upon its placement)?
Look at the picture below. North pole is green and South pole is red. All needles are lined up in the direction of the local external magnetic field. Three of them are identified by arrows. Towards what pole do the needles identified by arrows point? What about the rest of the needles not identified by arrows? Sort it out in your head and tell me.

Darshit Sharma said:
Sir, could you please provide me with a visual example where the needle will, in one case, point towards the south and, in another case, towards the north pole (depending upon its placement)?Before all our discussions, I used to think that the needle would always point towards the north of a bar magnet (not Earth's but just a simple one lying on the table) and the location or the direction of the North pole may change as per the placement of the magnetic needle. I doubt that I am mistaken.

However, there's another question:

View attachment 338721Now, I find myself sufficiently adept to answer subpart (ii). However, I am still confused about (i) and (iii). I know you are trying to make me understand but I am unable to relate to it; I don't know why it is so.I have heard about the "AMPERE SWIMMING RULE" which used to say something like if you imagine yourself swimming along the current such that the current enters from your feet and leaves from your head then your left hand gives the direction of the magnetic field at that point.
but that used to be the case when the needle was above the wire and here the needle is below the wire, so technically what I have learnt till now, is that the direction the needle's pointing should be reversed, i.e. if according to the image, first, it should be towards the East if the needle is above the wire but since for the (i) the needle is below the wire, it should then point towards my right, i.e. towards the West.
So according to this "SNOW rule" and "AMPERE SWIMMING RULE" I concluded the following:
(I) West (ii) EastOnce again, as always, I was wrong in my reasoning, and the answer key says just the opposite (I) East (ii) WestI don't know where I went wrong, I tried to use the Right hand thumb rule but was unable to do so because I was confused whether to imagine the needle below in 3-D or in 2-D as @Delta2 told me that we have to think in 2D but if we think 2-D then the direction of the magnetic field do come vertically below the needle. How could the needle point that way?

Confused :(
First of all don't post a separate problem on the same thread as another problem. If you have a separate problem, post it on a separate thread.

Secondly, I strongly suggest that you need to internalize what I have said many time already: Magnetic needles line up so that their South-to-North direction is parallel to the local magnetic field. They DO NOT point to a particular point in space. That idea is illustrated in the picture in post #15.

Thirdly, it follows that if you want to figure out in what direction a magnetic needle will point, you first have to figure out the direction of the magnetic field at the point you place the needle and then turn the needle parallel to that direction. That's all. Ampere's swimming rule and SNOW are completely unnecessary and, in my opinion, confusing nonsense. If you want to learn how to figure out the direction and magnitude of the magnetic field due to a long wire read this.

Fourthly, your second question is another one of those poorly phrased questions that result in ambiguity of interpretation. It says that "The diagram below shows a magnetic needle kept just below the conductor AB. What on Earth does "just below" mean? There could be two interpretations assuming that the plane of the loop is in the plane of the screen.
1. The accompanying figure suggests that the needle is in the plane of the loop and displaced at some distance in the eastward direction. It is below in the sense that it is towards the bottom of the screen. This is reproduced below left in the attached figure.
2. It could also be below AB at some distance farther into the screen from the plane of the loop as shown in the attached figure below right.
Judging from the given answer here, the intended interpretation is the second one. If you wish to pursue this further, please post on a separate thread as I already indicated.

Last edited:
Darshit Sharma and MatinSAR
kuruman said:
Look at the picture below. North pole is green and South pole is red. All needles are lined up in the direction of the local external magnetic field. Three of them are identified by arrows. Towards what pole do the needles identified by arrows point? What about the rest of the needles not identified by arrows? Sort it out in your head and tell me.
Sir I realised my mistake of posting 2nd question in the same thread.
@kuruman

Continuing with this one, I deeply analysed everything and since the magnetic field is from north to South for both the solenoids. The needle should point in the direction of the magnetic field which is between the two south poles.
So I finally concluded that the green part of my needle is the north pole of the needle.
Could you tell me which (the red or the green part) is the north pole of the magnetized needle?
And is the polarity of my solenoids correctly labelled?

Darshit Sharma said:
So I finally concluded that the green part of my needle is the north pole of the needle.
That is correct.

Darshit Sharma

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