Need help with the magnetic field generated by this current distribution

[Magnetosphere]

Homework Statement

A DC current is flowing between two electrodes through a iron disk medium. Positive is attached to the copper shaft of the disc and the negative is attached to the outer brass periphery of the disk. The radius of the disk is 2,54mm (1 inch) and the height of the disk is 1cm. How does the magnetic field look/behave when a DC current is applied to the disk?

Homework Equations

Right hand rule

The Attempt at a Solution

I have searched online for the answer and made a few attempts at figuring it out myself but without any success. I can´t wrap my head around it.

 

[berkeman]

Welcome to the PF.

Homework Statement

A DC current is flowing between two electrodes through a iron disk medium. Positive is attached to the copper shaft of the disc and the negative is attached to the outer brass periphery of the disk. The radius of the disk is 2,54mm (1 inch) and the height of the disk is 1cm. How does the magnetic field look/behave when a DC current is applied to the disk?

Homework Equations

Right hand rule

The Attempt at a Solution

I have searched online for the answer and made a few attempts at figuring it out myself but without any success. I can´t wrap my head around it.View attachment 235599

Can you show us a sketch of the current distribution in the disc? Then start with one piece of that current distribution, and sketch the B-field from it. Then add more and more pieces of the current distribution to see what the overall total field might look like...

 

[Magnetosphere]

T

Welcome to the PF.

Can you show us a sketch of the current distribution in the disc? Then start with one piece of that current distribution, and sketch the B-field from it. Then add more and more pieces of the current distribution to see what the overall total field might look like...

Hi and thank you for the reply!
The current distribution is simple, it is moving from the copper axis outward through the iron to the brass ring. I guess the electrical lines would look like spokes in a bicykle.

 

[berkeman]

Thread is in Moderation for a bit to sort this out...

 

[berkeman]

Thread is re-opened.

 

[berkeman]

The current distribution is simple, it is moving from the copper axis outward through the iron to the brass ring. I guess the electrical lines would look like spokes in a bicykle.

Can you sketch the B-field for one of those spokes of current? Then sketch the B-field from 4 spokes, 90 degrees apart on the disc. Then think about what happens to the B-field as you fill in more and more spokes...

 

[Magnetosphere]

Can you sketch the B-field for one of those spokes of current? Then sketch the B-field from 4 spokes, 90 degrees apart on the disc. Then think about what happens to the B-field as you fill in more and more spokes...

Hi, thanks for the input. Yes I can visualize/draw the electrical field lines coming out from the axis going through the iron to the periphery of the disk and the magnetic forces for each individual line, I just can´t wrap my head around how the combined magnetic force will look from a distance. Just like one can imagine the total magnetic field coming out from a magnet. Since the electrical field i spreading out in all directions 360 degrees around its own axis I can´t understand how the total magnetic field will look. I wish someone could draw it and post it, no opinions or guesses.

 

[Magnetosphere]

This is a physics forum, doesn't anyone know the answer to this question?

 

[berkeman]

This is a physics forum, doesn't anyone know the answer to this question?

I have an idea of what it would look like (with some assumptions), but I was hoping someone else would post first.

Can you show us your best sketch?

 

[rude man]

Start with ∇xH = j
H = B/μ
j = current density.
You know j everywhere in the iron.

 

[kuruman]

My online search produced this link
https://ieeexplore.ieee.org/document/996131
It looks like a computational solution is required.

 

[rude man]

My online search produced this link
https://ieeexplore.ieee.org/document/996131
It looks like a computational solution is required.

Not to mention elliptic integrals.
Not a subject for intro physics (not a nice one for upper-class physics either!).

 

[Magnetosphere]

I have an idea of what it would look like (with some assumptions), but I was hoping someone else would post first.

Can you show us your best sketch?

Thanks for the interest. I can´t sketch the magnetic field, can´t wrap my head around it. What I am imagining is a magnetic vortex field. Please share your thoughts.

 

[Magnetosphere]

I

Start with ∇xH = j
H = B/μ
j = current density.
You know

Not to mention elliptic integrals.
Not a subject for intro physics (not a nice one for upper-class physics either!).

I know, that´s what I thought, is this a topic for intro physics? As I see it it is a little harder than intro.

 

[Magnetosphere]

My online search produced this link
https://ieeexplore.ieee.org/document/996131
It looks like a computational solution is required.

I am not sure this is what I am talking about, in this paper I believe they are talking about a radial array of magnets, I am talking about radially dispersed electrical currents and their combined magnetic field.

 

[kuruman]

I am not sure this is what I am talking about, in this paper I believe they are talking about a radial array of magnets, I am talking about radially dispersed electrical currents and their combined magnetic field.

Isn't the abstract mentioning what you are interested in? I have pasted it for your convenience but I have not read the full paper.

Abstract:
In this paper, new expressions are presented for three-dimensional magnetic-field calculation for a massive disk currying (sic) radial currents. These expressions have been obtained in analytical form as functions of incomplete elliptical integrals (of the first, second, and third kind) and an integral to be solved numerically. This approach enables one to easily calculate the magnetic field everywhere in space at reduced computational cost. In addition, it can be employed to calculate the magnetic field in conductor disk configurations involving complicated geometry as well as to evaluate their self and mutual inductance.

 

[Magnetosphere]

Yes, I understand and I am glad you are here, I believe they are talking about magnetic currents, not electric currents. I read the paper further down and as I understood it they were talking about a radial array of magnets. I am talking about a radial array of electric current.

 

[Magnetosphere]

I have an idea of what it would look like (with some assumptions), but I was hoping someone else would post first.

Can you show us your best sketch?

Here is my best sketch. Please keep in mind in this image the magnetic fields do not combine or repel, they overlap. This image is most probably very different from the truth

.

 

[kuruman]

I think magnetic fields "combine" in the sense that at any point in space the magnetic field is the vector sum of the contributions $d\vec B$ from all current elements to that point. Therefore, they cannot intersect. Also, it is a law of nature that magnetic field lines form closed loops.

 

[Magnetosphere]

 

[Magnetosphere]

In my opinion it looks pretty but is completely false.

 

[Charles Link]

I looked at this problem when it was first posted, and I did not have a good answer for it, or I would have responded sooner. You can't simply discard the magnetic field caused by the current in the wires external to the disc. Meanwhile, with iron, the response can be very large to even rather weak magnetic fields. I could not come up with a clear qualitative picture in my head from using Biot-Savart of exactly how the magnetic field might look in the disc=it appears it might be in one direction in the upper half of the disc, and in the opposite direction in the lower portion. In any case, I think the problem is non-trivial, and I don't know that it even has a well-defined answer=minor alterations in the incoming and outgoing wires could have a huge effect on the result.

 

[Magnetosphere]

Thanks for the input. I am not sure if we are talking about the same thing. How will the magnetic field look around the disk from a distance? Just like one can draw the magnetic field around a magnet I would like to see an image of the magnetic field around this disk. Imagine 50 volts at 1 amp going through the disk, how will the magnetic field look?

Not forgetting magnetic pole direction, in this particular setup with positive being the axis of the disk.

 

[berkeman]

Nice sketches! What software did you use to make them?

How will the magnetic field look around the disk from a distance?

I'm not sure about far away (there may be very little net field far away compared to the dimensions of the disc), but near the disc, it looks like the vertical B-fields cancel, and you are left with a swirling magnetic field in the toriodal direction above and below the disc, no? Interesting problem...

 

[Charles Link]

Thanks for the input. I am not sure if we are talking about the same thing. How will the magnetic field look around the disk from a distance? Just like one can draw the magnetic field around a magnet I would like to see an image of the magnetic field around this disk. Imagine 50 volts at 1 amp going through the disk, how will the magnetic field look?

The magnetic field external to the disc would very likely depend on how the iron responded to the internal fields. Once the distribution of the magnetization $M$ is determined, the external magnetic field can be computed, at least numerically, using the magnetic pole theory, with magnetic pole density $\rho_m=-\nabla \cdot M$. The $H$ is then computed using the inverse square law. Computing the magnetization $M$ as a function of position in the disc looks very difficult though. It would need to be a self-consistent problem, with the response assumed to be proportional to the magnetic field strength. $\\$ The geometry of this problem looks simple enough, but it is not a simple problem.

 

[Magnetosphere]

Nice sketches! What software did you use to make them?

I'm not sure about far away (there may be very little net field far away compared to the dimensions of the disc), but near the disc, it looks like the vertical B-fields cancel, and you are left with a swirling magnetic field in the toriodal direction above and below the disc, no? Interesting problem...

Hi, thanks. I used sketchup. Yes, I agree, I was thinking of a vortex too. The question is, since the electron flow is going into the axis from the outer periphery of the disk, which side of the disk is north/south if the disk even has poles? Which I imagine it does.

 

[Magnetosphere]

The magnetic field external to the disc would very likely depend on how the iron responded to the internal fields. Once the distribution of the magnetization $M$ is determined, the external magnetic field can be computed, at least numerically, using the magnetic pole theory, with magnetic pole density $\rho_m=-\nabla \cdot M$. The $H$ is then computed using the inverse square law. Computing the magnetization $M$ as a function of position in the disc looks very difficult though. It would need to be a self-consistent problem, with the response assumed to be proportional to the magnetic field strength. $\\$ The geometry of this problem looks simple enough, but it is not a simple problem.

I totally agree with you, you explained the dilema well. Does the disk have a north and a south pole?

 

[Charles Link]

I totally agree with you, you explained the dilema well. Does the disk have a north and a south pole?

For north and south pole, I don't see any obvious ones. That would be a good place to start with a qualitative solution if you could demonstrate some kind of direction in the magnetization, but from what I can see, the magnetization $\vec{M}$ might run in a circle, (around the whole disc), in the upper part of the disc, and in an opposite circle on the lower part. In that case, It appears poles might be virtually absent.

 

[Magnetosphere]

I looked at this problem when it was first posted, and I did not have a good answer for it, or I would have responded sooner. You can't simply discard the magnetic field caused by the current in the wires external to the disc. Meanwhile, with iron, the response can be very large to even rather weak magnetic fields. I could not come up with a clear qualitative picture in my head from using Biot-Savart of exactly how the magnetic field might look in the disc=it appears it might be in one direction in the upper half of the disc, and in the opposite direction in the lower portion. In any case, I think the problem is non-trivial, and I don't know that it even has a well-defined answer=minor alterations in the incoming and outgoing wires could have a huge effect on the result.

I misunderstood you the first time so I deleted my response. I think you can discard the magnetic field in the wires external to the disk, imagine the voltage and current so high that the magnetic field from the wires becomes insignificant compared to the magnetic field from the disk.

 

[Magnetosphere]

For north and south pole, I don't see any obvious ones. That would be a good place to start with a qualitative solution if you could demonstrate some kind of direction in the magnetization, but from what I can see, the magnetization $\vec{M}$ might run in a circle, (around the whole disc), in the upper part of the disc, and in an opposite circle on the lower part. In that case, It appears poles might be virtually absent.

LOL, this is what i can´t wrap my head around.

 

[Magnetosphere]

For north and south pole, I don't see any obvious ones. That would be a good place to start with a qualitative solution if you could demonstrate some kind of direction in the magnetization, but from what I can see, the magnetization $\vec{M}$ might run in a circle, (around the whole disc), in the upper part of the disc, and in an opposite circle on the lower part. In that case, It appears poles might be virtually absent.

To determine magnetic poles of the disk one would assume to follow the right hand rule, when I imagine it it seems north is the top of the disk.

 

[Charles Link]

LOL, this is what i can´t wrap my head around.

An example of this is a toroidal solenoid with an iron core. The magnetization $M$ goes around the toroid in a circle. This generates virtually no magnetic field outside the toroid, but the field is very strong inside. Meanwhile there are no magnetic poles. $\nabla \cdot M=0$ or very close to it.

 

[Magnetosphere]

An example of this is a toroidal solenoid with an iron core. The magnetization $M$ goes around the toroid in a circle. This generates virtually no magnetic field outside the toroid, but the field is very strong inside. Meanwhile there are no magnetic poles. $\nabla \cdot M=0$ or very close to it.

Yes, but a toroidal solenoid does not have a parallel electric field like this disk. Here the electric force is at the same angle through the medium.

 

[Charles Link]

You have a very interesting problem, but I would suggest getting a very good proficiency with some of the more well-known magnetostatic problems, such as cylindrical magnets, and the problem of a magnetized sphere with uniform magnetization before attempting something of this degree of difficulty. See e.g. https://www.physicsforums.com/threa...perature-relationship-in-ferromagnets.923380/ You might find the students' experiment of some interest. See also post 21, where I used a boy scout compass to measure the magnetic field strength of a cylindrical magnet.

 

[Magnetosphere]

You have a very interesting problem, but I would suggest getting a very good proficiency with some of the more well-known magnetostatic problems, such as cylindrical magnets, and the problem of a magnetized sphere with uniform magnetization before attempting something of this degree of difficulty. See e.g. https://www.physicsforums.com/threa...perature-relationship-in-ferromagnets.923380/ You might find the students' experiment of some interest. See also post 21, where I used a boy scout compass to measure the magnetic field strength of a cylindrical magnet.

I need to find out that´s why I found this place. I suspect the answer is easier than I think, I just can´t see it on my own. I strongly suspect the disk has poles, that´s really all I need to know, does it have poles and where are they in relationship to the axis?

 

[Charles Link]

I need to find out that´s why I found this place. I suspect the answer is easier than I think, I just can´t see it on my own. I strongly suspect the disk has poles, that´s really all I need to know, does it have poles and where are they in relationship to the axis?

I have seen a lot of magnetostatic problems, but this one is new to me. Maybe there is a simple answer to it, but it isn't immediately obvious to me what that might be.

 

[Magnetosphere]

 

[kuruman]

I strongly suspect the disk has poles ...

Why? In what direction would the South-North pole direction be? The only possibility would be along the disk axis. Now the wire going into the disk cannot generate a field along that axis and the field generated by a radial current flowing in one direction would be canceled by the radial current flowing in the opposite direction at 180^o from it.

Consider this. Very close to the plane of the disk at height $h<<<R$ above it, the disk looks like an infinite plane. What is the magnetic field due to an infinite plane? Start from there and see if you can extend this picture to distances not as close to the disk.

 

[Magnetosphere]

Why? In what direction would the South-North pole direction be? The only possibility would be along the disk axis. Now the wire going into the disk cannot generate a field along that axis and the field generated by a radial current flowing in one direction would be canceled by the radial current flowing in the opposite direction at 180^o from it.

Consider this. Very close to the plane of the disk at height $h<<<R$ above it, the disk looks like an infinite plane. What is the magnetic field due to an infinite plane? Start from there and see if you can extend this picture to distances not as close to the disk.

I suspect only because the electric field is at a plane, one would conclude magnetism 90 degrees to that plane. You are right that the current is flowing in the opposite direction, that is bothering me. I have a hard time imagining that part with infinite plane, that´s above my capabilities.

 

[kuruman]

I suspect only because the electric field is at a plane, one would conclude magnetism 90 degrees to that plane. You are right that the current is flowing in the opposite direction, that is bothering me. I have a hard time imagining that part with infinite plane, that´s above my capabilities.

https://www.physics.byu.edu/faculty/christensen/Physics%20220/FTI/30%20Sources%20of%20the%20Magnetic%20Field/30.14%20Magnetic%20field%20of%20an%20infinite%20current%20sheet.htm

 

[Magnetosphere]

https://www.physics.byu.edu/faculty/christensen/Physics%20220/FTI/30%20Sources%20of%20the%20Magnetic%20Field/30.14%20Magnetic%20field%20of%20an%20infinite%20current%20sheet.htm

Thanks, an infinite plane would mean there is no in or out, the magnetic field could not complete its loop as I see it. But the disk is not an infinite plane.

 

[kuruman]

Thanks, an infinite plane would mean there is no in or out, the magnetic field could not complete its loop as I see it. But the disk is not an infinite plane.

You missed the point. If you are one micron above a disk that is 10 cm in radius at distance 5 cm the center, the ends and the center of the disk are very very far away relative to your height above the plane. For all intents and purposes the disk looks like an infinite plane and the B-field locally is parallel to the surface and perpendicular to the radial direction. Now if you keep the distance of 5 cm constant and you go around the circle that picture is maintained. So what do you think the closed loop magnetic field lines look like at least very near the surface of the disk?

 

[Tom.G]

Suspiciously similar to a Homopolar generator. Anyone have access to Maxwell simulation software?

 

[Magnetosphere]

You missed the point. If you are one micron above a disk that is 10 cm in radius at distance 5 cm the center, the ends and the center of the disk are very very far away relative to your height above the plane. For all intents and purposes the disk looks like an infinite plane and the B-field locally is parallel to the surface and perpendicular to the radial direction. Now if you keep the distance of 5 cm constant and you go around the circle that picture is maintained. So what do you think the closed loop magnetic field lines look like at least very near the surface of the disk?

When I visualize your description I see magnetic forces going in a circle around the axis and closing the magnetic loop just outside the periphery of the disk (this is most probably wrong). I am not a scientists and not used to this stuff. The shaft being the positive electrode, what direction would the magnetic lines go? I really have no idea. How do you think the closed loop magnetic field lines look like at least very near the surface of the disk? Is this really a tough question or there is clear yes or no to whether the disk has clearly defined poles? I am a complete amateur, that´s why I came here in hopes to get an answer from a scientist.

 

[Magnetosphere]

So much text written and not a single step forward, very typical for forums. I feel like all posts should be removed as they really do not contribute to any forward movement, not that I don't appreciate peoples involvement, it´s just that all those words do not bring anyone looking for a similar problem any closer to the answer, too much text to go through without the award one is looking for.

 

[berkeman]

So much text written and not a single step forward

Actually, you have a pretty good qualitative idea now of what the B-field looks like close to the disc. For a better solution, numerical simulation software has been suggested several times. Do you have an application in mind? Or is this just for general interest?

 

[Magnetosphere]

Actually, you have a pretty good qualitative idea now of what the B-field looks like close to the disc. For a better solution, numerical simulation software has been suggested several times. Do you have an application in mind? Or is this just for general interest?

It´s all wild guesses and I am not convinced my idea how the b field looks like is right at all. Numerical simulation has been suggested but that is an overkill. I can´t spend days learning a new software when all I need to know whether the disk has poles or not. What I want to do is run dc voltage through the disk and align all magnetic forces accordingly to the electric current with the help of a lab magnet.

 

[berkeman]

What I want to do is run dc voltage through the disk and align all magnetic forces accordingly to the electric current with the help of a lab magnet.

What do you mean by "align the magnetic forces"? Do you mean you want to magnetize the iron disc in the radial direction?

 

[Magnetosphere]

No, the radial direction is the direction of the electricity, I need to place a lab magnet in line with the magnetic forces that are produced by the electricity.

 

[berkeman]

No, the radial direction is the direction of the electricity, I need to place a lab magnet in line with the magnetic forces that are produced by the electricity.

When the B-field lines close on themselves (as it appears they do above and below your disc), you could place a small bar magnet lined up parallel to the B-field lines, I guess.

Are you familiar with the B-field lines inside a toroid? The circulating B-field inside looks similar to what it probably looks like above your disc...

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/tor.png