Magnetic field pointing into a normal magnetized compass needle

[Darshit Sharma]

Homework Statement

In which direction will the needle point?

Relevant Equations

Right Hand Thumb Rule

I was just thinking that if we keep the wire in, suppose, XZ plane and the magnetized needle also in XZ plane. Then in which direction will the needle point? we're going to have either +j cap or -j cap direction by drawing out the tangent at the point where the needle is kept. But a needle could only rotate in 2D I guess. If we were to erect the compass i.e. the base of the compass would be in a plane perpendicular to the wire while it is currently in the same plane as the wire, the needle would be free to show the +j cap or - j cap direction but what now?

(Skip the above piece of text if it is not comprehendible to you.)

This is what I am trying to ask. The thing is that the needle is kept in the same plane as the wire but it is perpendicular to the plane of the magnetic field (shown in the diagram) so the magnetic field's direction is pointing outwards to the plane of the needle but how will we able to know that using a needle.

There is no complication of any specific XZ plane or such things. The things are simple and as follows:

• There is a simple current-carrying wire.
• There is an associated magnetic field with it in the plane perpendicular to the wire.
• There is a magnetized needle kept in a plane perpendicular to the plane containing magnetic field lines. (The needle is essentially kept in the same plane as the wire with which we started)

The question is as follows:

• Since the tangent to the magnetic field lines point perpendicularly in or out (out in the case of the image), in which direction would the magnetized needle point?
• Thoughts in my mind: If the needle were to be in the same plane as the magnetic field (which is the plane perpendicular, not the same, as of the original wire.) it would have pointed in the direction of the magnetic field at that (or any) point, but how do we make the needle turn in a 3D space when it is only allowed to orient itself in a 2D space.

I hope the question is not as vague as before.

J-cap direction is this thing: the direction of the y-axis

 

[berkeman]

Is there a figure that goes with this question? Please use the "Attach files" link below the Edit window to upload a PDF or JPEG version of the figure. Thanks.

Also, what are the Relevant Equations for figuring out which way a (magnetized or non-magnetized) needle will point in a magnetic field?

(and what is "RHTR"?)

 

[kuruman]

What are you talking about? Please post a picture and clearly explain what it is showing. It's OK to assume that your compass needle is mounted so that it could rotate at any angle.

 

[Darshit Sharma]

What are you talking about? Please post a picture and clearly explain what it is showing. It's OK to assume that your compass needle is mounted so that it can rotate at any angle.

Done and Sir do I need to open another thread to ask if the SNOW rule and the ampere swimming rule are completely wrong? Or it will be ok to continue that in my old thread? Just that is the last thing there it was connected so I asked there.

 

[berkeman]

Homework Statement: In which direction will the needle point?
Relevant Equations: Right Hand Thumb Rule

we re going to have either +j cap or -j cap direction by drawing out the tangent at the point where the needle is kept.

What's a "j cap" direction? Is the needle magnetized or non-magnetized? It would also help if you could make a better 3-D drawing including the coordinate axes (or better yet upload a figure from your textbook on this question).

do I need to open another thread to ask if the SNOW rule and the ampere swimming rule are completely wrong?

Sorry, what in the world are those?

 

[berkeman]

Where in this figure are you placing your needle?

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

 

[Darshit Sharma]

Where in this figure are you placing your needle?

perpendicular to the plane of the magnetic field.

 

[berkeman]

perpendicular to the plane of the
magnetic field.

So parallel to the wire? That will be a pretty unstable position, but if balanced perfectly the ferrous needle would not rotate. It would do something else instead -- can you say what and why?

 

[Darshit Sharma]

Sorry, what in the world are those?

The condensation of my doubt regarding them is the correctness of this explanation on this site.

The deflection should be towards the right if I ain't mistaken.

 

[Darshit Sharma]

So parallel to the wire? That will be a pretty unstable position, but if balanced perfectly the ferrous needle would not rotate. It would do something else instead -- can you say what and why?

Yes yes. Maybe it will rest in any direction? like some kind of "SYSTEM ERROR" for the needle?

And sir (addressed to either (or both) of you @berkeman or(and) @kuruman) are the polarities or the solenoids correct? I had opened a thread previously but it generated a lot of messy replies because I wasn't able to understand a minor but vital thing which led to not properly arriving at the solution.

The original question was a bit suppressed by my vague doubts, i.e. the first and the original question in the thread below. Could you tell me which (the red or the green part) is the north pole of the magnetized needle?

According to me, green.

Also would you like to check if what I said in my last post on this thread is true? https://www.physicsforums.com/threa...le-between-two-solenoids.1059087/post-6987839

 

[PhDeezNutz]

I think the needle will rotate downward, M is the magnetic dipole (the needle)

 

[kuruman]

The thing is that the needle is kept in the same plane as the wire

Here is a picture showing current in a long wire coming out of the screen. If you place a magnetic needle in the same plane as the wire (seen edge-on as a gray line), it will point up if it is on the right side of the wire and down if it is on the left side of the wire.

Your picture in post #1 should look like what I show below. Note that the current is reversed from yours because I couldn't find a picture on the web with the current up. Note that the needle is in a plane perpendicular to the wire.

 

[PhDeezNutz]

Oh wow I totally misunderstood the question. But the idea is the same.

 

[berkeman]

Oh wow I totally misunderstood the question.

How is that possible? Everything is so crystal clear...

 

[PhDeezNutz]

Alright here is a correction

$\vec{\tau} = \vec{m} \times \vec{B}$

$\vec{m}$ is parallel to the wire (pointing up)

$\vec{B}$ points into the page (That's what a X'd circle means)

Take the cross product and $\vec{\tau}$ points inward towards the wire. Meaning it spins into the page to align with the magnetic field.

There we go. I think this is all good now. Apologies to OP.

 

[Darshit Sharma]

Here is a picture showing current in a long wire coming out of the screen. If you place a magnetic needle in the same plane as the wire (seen edge-on as a gray line), it will point up if it is on the right side of the wire and down if it is on the left side of the wire.View attachment 338849

Your picture in post #1 should look like what I show below. Note that the current is reversed from yours because I couldn't find a picture on the web with the current up. Note that the needle is in a plane perpendicular to the wire.View attachment 338857

Okok Done question is solved. Thanks sir

 

[Darshit Sharma]

Alright here is a correction View attachment 338858$\vec{\tau} = \vec{m} \times \vec{B}$

$\vec{m}$ is parallel to the wire (pointing up)

$\vec{B}$ points into the page (That's what a X'd circle means)

Take the cross product and $\vec{\tau}$ points inward towards the wire. Meaning it spins into the page to align with the magnetic field.

There we go. I think this is all good now. Apologies to OP.

Thanks sir