Need help with the magnetic field generated by this current distribution

[Magnetosphere]

@Tom.G just told you in #58.

He told me the technique for searching not the search words he used.

 

[kuruman]

He told me the technique for searching not the search words he used.

One more time,

The search string is everything following the "&q=" in the Google link above.

What follows "&q=" in https://www.google.com/search?&q=magnetic+field+of+homopolar+generators ?

 

[Magnetosphere]

So in this instance the search words are: magnetic field of homopolar generators, that's my point, I did not even know of such a word as homopolar generator. That technique is not even necessary if you know the word "homopolar".

 

[kuruman]

So in this instance the search words are: magnetic field of homopolar generators, that's my point, I did not even know of such a word as homopolar generator.

Now you do. It's called "learning".

 

[Magnetosphere]

Kuruman, please.. The point I am making is that unless you know what words to use you won´t find smack using the best technique. English is not my first language and even if it were I still need to know WHAT to search for, what words to use.

 

[kuruman]

I understand your point and I agree with it, so please understand mine which is just as obvious as yours: you cannot possibly know something unless you learn it first.

 

[berkeman]

BTW @Magnetosphere -- in the setup as shown in your original diagram, the outer conducting band will not have a substantially greater conductivity compared to the iron disc. So the current distribution you get in the iron disc will not necessarily be mostly radial. I think it will be concentrated between the inner conductor and the tap point on the outer conducting band where the 2nd wire comes off. So you will esentially get current only in the part of the disc between the inner and outer wires, IMO. The iron filings will show that current distribution, instead of swirling like they would for a uniform radial current distribution.

 

[Magnetosphere]

I understand your point and I agree with it, so please understand mine which is just as obvious as yours: you cannot possibly know something unless you learn it first.

I really have no idea what point you are making, I am aware one needs to learn first before one knows something. All I was asking was what search words he used and that search technique is only useful if you also know what words to search for. This discussion really doesn't belong here so i suggest we focus on solving the problem.

 

[Magnetosphere]

BTW @Magnetosphere -- in the setup as shown in your original diagram, the outer conducting band will not have a substantially greater conductivity compared to the iron disc. So the current distribution you get in the iron disc will not necessarily be mostly radial. I think it will be concentrated between the inner conductor and the tap point on the outer conducting band where the 2nd wire comes off. So you will esentially get current only in the part of the disc between the inner and outer wires, IMO. The iron filings will show that current distribution, instead of swirling like they would for a uniform radial current distribution.

View attachment 235978

Thanks for the input. The only reason I have a brass ring is because the experiment I am going to conduct has one. I will prepare the iron disk this week and take a few pictures of the iron filings on cardbord.

 

[Charles Link]

I really thought this was an easy question, some scientist at some forum will probably be able to answer within a day or so is what I thought. It looks like I will have to do the experiment. I do not have such a disk and will have to make it, that is another reason why I wanted to save time by asking, I really thought it was as easy as asking how does a magnetic field look around a regular magnet. I still think though that this is an easy question, however everything seems difficult until you know it. Will post pictures of the experiment.

I expect the external magnetic field to be rather minimal for this case even with the iron disc as opposed to copper. The conclusion from that is you won't get the magnetic poles that you are predicting. Had this particular scenario been a useful one, it would presently be in widespread use as a laboratory demonstration or even have industrial applications. I would be very surprised if you find that it produces any kind of substantial magnetic fields external to the device.

 

[Charles Link]

I expect the external magnetic field to be rather minimal for this case even with the iron disc as opposed to copper. The conclusion from that is you won't get the magnetic poles that you are predicting. Had this particular scenario been a useful one, it would presently be in widespread use as a laboratory demonstration or even have industrial applications. I would be very surprised if you find that it produces any kind of substantial magnetic fields external to the device.

Additional comment: The geometry that they have found to be extremely useful is to wrap insulated wire windings around an iron cylinder and run a current through the windings to make an electromagnet. The magnetic fields for this case are quite straightforward and are very much standard textbook material. Had you asked about this case, you most likely would have gotten some very good and very detailed answers. In this electromagnet case, you do get two well defined poles on the end faces of the iron cylinder. $\\$ The electromagnet is an extremely interesting problem, and the magnetic fields can be precisely computed in two different ways: 1) By a magnetic pole method 2) By a magnetic surface current method, that really describes the underlying physics much better than the pole method.$\\$ [Magnetic surface currents result on the iron core from a uniform magnetization throughout the iron. These surface currents go around the iron cylinder and are (approximately) 1000 x stronger than the current in the windings and in the same direction as the current in the windings, and they arise, not because of the close proximity to the current in the windings, but actually bacause of the uniform magnetization that occurs in the iron cylinder as a result of a uniform magnetic field that occurs from the windings. Without the iron core, these windings make a very well known solenoid geometry that generates a uniform magnetic field inside the cylinder along its axis. With the iron core, the magnetic field is stronger in the core by a factor of 1000 because of the magnetic field generated by the magnetic surface currents. The magnetic flux lines go through the iron core and emerge out one end , the north pole, and loop around and go back into the magnet at the south pole. $\\$ The equations of the pole method, (in particular the equation $\vec{B}=\mu_o \vec{H}+\vec{M}$), might lead one to believe that the magnetic field $B$ in the iron core is created by the magnetization $M$, but in fact, the surface current method shows that the magnetic field in the iron core actually results from the surface currents that result from the magnetization $M$ when it encounters the surface boundary.] $\\$ $\\$ Both methods get the exact same answer for the magnetic field. The pole method is mathematically simpler, but, in general, magnetic fields are caused by the motion of electrical charges (which are contained in the surface current method). The static pole method, in any case, is a very good mathematical shortcut. It has been mathematically proven that these two methods give identical results.

 

[Magnetosphere]

I expect the external magnetic field to be rather minimal for this case even with the iron disc as opposed to copper. The conclusion from that is you won't get the magnetic poles that you are predicting. Had this particular scenario been a useful one, it would presently be in widespread use as a laboratory demonstration or even have industrial applications. I would be very surprised if you find that it produces any kind of substantial magnetic fields external to the device.

Great input! That is exactly what I was thinking, I won´t be able to produce a significantly large magnetic field to notice it, not with the puny power I have access to. I will probably drop the disk experiment, but I still need to know how the field looks.

 

[Magnetosphere]

Additional comment: The geometry that they have found to be extremely useful is to wrap insulated wire windings around an iron cylinder and run a current through the windings to make an electromagnet. The magnetic fields for this case are quite straightforward and are very much standard textbook material. Had you asked about this case, you most likely would have gotten some very good and very detailed answers. In this electromagnet case, you do get two well defined poles on the end faces of the iron cylinder. $\\$ The electromagnet is an extremely interesting problem, and the magnetic fields can be precisely computed in two different ways: 1) By a magnetic pole method 2) By a magnetic surface current method, that really describes the underlying physics much better than the pole method.$\\$ [Magnetic surface currents result on the iron core from a uniform magnetization throughout the iron. These surface currents go around the iron cylinder and are (approximately) 1000 x stronger than the current in the windings and in the same direction as the current in the windings, and they arise, not because of the close proximity to the current in the windings, but actually bacause of the uniform magnetization that occurs in the iron cylinder as a result of a uniform magnetic field that occurs from the windings. Without the iron core, these windings make a very well known solenoid geometry that generates a uniform magnetic field inside the cylinder along its axis. With the iron core, the magnetic field is stronger in the core by a factor of 1000 because of the magnetic field generated by the magnetic surface currents. The magnetic flux lines go through the iron core and emerge out one end , the north pole, and loop around and go back into the magnet at the south pole. $\\$ The equations of the pole method, (in particular the equation $\vec{B}=\mu_o \vec{H}+\vec{M}$), might lead one to believe that the magnetic field $B$ in the iron core is created by the magnetization $M$, but in fact, the surface current method shows that the magnetic field in the iron core actually results from the surface currents that result from the magnetization $M$ when it encounters the surface boundary.] $\\$ $\\$ Both methods get the exact same answer for the magnetic field. The pole method is mathematically simpler, but, in general, magnetic fields are caused by the motion of electrical charges (which are contained in the surface current method). The static pole method, in any case, is a very good mathematical shortcut. It has been mathematically proven that these two methods give identical results.

Great stuff!
"Had you asked about this case, you most likely would have gotten some very good and very detailed answers.", yes, my scenario is different though.
I have built an electromagnet once, 2000 windings and water cooled, worked really well. I am not so much interested in mathematics as I am in a visual representation of the field. The math is far above my head.
"you do get two well defined poles on the end faces of the iron cylinder." could you make a sketch just so there is no misunderstanding?

 

[Charles Link]

Great input! That is exactly what I was thinking, I won´t be able to produce a significantly large magnetic field to notice it, not with the puny power I have access to. I will probably drop the disk experiment, but I still need to know how the field looks.

If you want to figure out what the magnetic field looks like, (to compute it yourself), a good place to start would be the description in post 71. It would take much effort to become an E&M expert, but if you went this route, I think you would find it interesting. Many physics people seem to have the misconception that all of the E&M was figured out around 1880-1900, so that it is much more important for them to spend their time studying things like quantum mechanics. The idea of the magnetic surface currents, at least in a very mathematical sense, I think is a somewhat recent one. In 1975-1980, we were taught the pole method, and the surface currents were only mentioned very quickly as an alternate theory that might work. In 2009-2012, I did a bunch of calculations that tied these two methods together. An E&M professor at the University of Illinois at Urbana-Champaign tells me they normally don't even teach the pole method anymore until graduate level courses. They now emphasize the surface current method.

 

[Charles Link]

See https://www.google.com/imgres?imgur...hUKEwjOo_jW-6nfAhUOW60KHfyICwYQ9QEwAHoECAcQBg $\\$ For the mathematics of this pole method, $\rho_m=-\nabla \cdot \vec{M}$. The result is that for uniform $\vec{M}=M_o \hat{z}$, there is no magnetic charge throughout the iron core, and on the end faces there is a (fictitious) magnetic surface charge density $\sigma_m=\vec{M} \cdot \hat{n}$, resulting in poles of $M_o A$ and $-M_o A$ on the two end faces of the cylinder, where $A$ is the area of the end face of the cylinder. $\\$ The $\vec{H}$ is computed from these poles using the inverse square law, just like $\vec{E}$ with $\epsilon_o$ replaced by $\mu_o$. To complete the calculation, $\vec{B}=\mu_o \vec{H}+\vec{M}$.

 

[berkeman]

"you do get two well defined poles on the end faces of the iron cylinder." could you make a sketch just so there is no misunderstanding?

Do you mean like this?

https://qph.fs.quoracdn.net/main-qimg-9cbd95a2b0e77c3d0c9431aaee3f6abc

EDIT -- Charles beat me to it (again!)

 

[Magnetosphere]

Do you mean like this?

https://qph.fs.quoracdn.net/main-qimg-9cbd95a2b0e77c3d0c9431aaee3f6abc

EDIT -- Charles beat me to it (again!)

Link doesn't work.

 

[berkeman]

You sure? Even in your quote it shows the picture...

 

[Magnetosphere]

Yeah, it doesn't show on my screen and if I go to the page the browser can't find it. I see it though on the second post but I can´t enlarge it.

 

[berkeman]

Lets see if this works better for you:

 

[Magnetosphere]

Lets see if this works better for you:

View attachment 235990

Looks great now!
it's good stuff and I believe I even used this when i build my own electromagnet some years ago, but does it somehow help in finding out how the magnetic field looks on my disk? Also, I´ve always wondered, where the current goes "in" is that the positive pole? The thing is, electrons travel from negative to positive right? So what do the arrows indicate, the flow of the electrons? Which would mean that the "in" side is negative and the "out", top in this picture, would be negative?

 

[kuruman]

This discussion really doesn't belong here so i suggest we focus on solving the problem.

I agree. Let's get back on track. As I understand the problem, you came up with this design and you want to know what the magnetic field outside the iron looks like, specifically if it has a north and south pole and where these might be. That is a valid question and has been partially answered in posts up to this one. What might be gathered so far is that a mathematical calculation is tricky and becomes trickier if one considers @berkeman 's observation in #67. You have also indicated most recently in #73 that you are not interested in math that is above you and that you are a visual person, so we have to set math aside. I will be curious to see the results of your iron filings experiment. Also, for a quick and easy way to visualize the magnetic field, you might wish to consider using a "magnaprobe". It is inexpensive and works well in mapping magnetic fields. Do a search on it.

 

[Magnetosphere]

I agree. Let's get back on track. As I understand the problem, you came up with this design and you want to know what the magnetic field outside the iron looks like, specifically if it has a north and south pole and where these might be. That is a valid question and has been partially answered in posts up to this one. What might be gathered so far is that a mathematical calculation is tricky and becomes trickier if one considers @berkeman 's observation in #67. You have also indicated most recently in #73 that you are not interested in math that is above you and that you are a visual person, so we have to set math aside. I will be curious to see the results of your iron filings experiment. Also, for a quick and easy way to visualize the magnetic field, you might wish to consider using a "magnaprobe". It is inexpensive and works well in mapping magnetic fields. Do a search on it.

Awsome stuff! Yes, you have pointed out very well all my concerns. I believe the easiest way is the iron filing test, a lot of current and voltage and a short bang and having a look with a microscope.
If the math for showing the magnetic field around the disk is a piece of cake for someone here I would be happy if that someone could to do the calculation and share their wisdom. As for poles I was hoping that one could attain an answer by pure reasoning setting all math aside. I will check out the magnaprobe, great tip!

 

[kuruman]

... a look with a microscope.

What's the diameter of the disk you are planning to make?

 

[berkeman]

Yes, you have pointed out very well all my concerns. I believe the easiest way is the iron filing test, a lot of current and voltage and a short bang and having a look with a microscope.

What's the diameter of the disk you are planning to make?

Rhut-rho...

 

[berkeman]

So what do the arrows indicate, the flow of the electrons?

The arrows in that diagram represent the normal convention of the flow of positive current, which is a convenience for expressing the opposite direction of the actual electron flow. Hope that makes sense.

 

[Magnetosphere]

Rhut-rho...

5cm diameter.

 

[Magnetosphere]

The arrows in that diagram represent the normal convention of the flow of positive current, which is a convenience for expressing the opposite direction of the actual electron flow. Hope that makes sense.

Thanks, does that mean that the negative electrode is at the top and the positive at the bottom in the diagram? I thought the direction of the arrows indicated electron flow, thinking it starts from negative and flows towards positive.

 

[kuruman]

Thanks, does that mean that the negative electrode is at the top and the positive at the bottom in the diagram? I thought the direction of the arrows indicated electron flow, thinking it starts from negative and flows towards positive.

In the figure in post #80, electric current goes in the direction of the red arrows, into the coil at the bottom and out of the coil at the top. That direction should be used in applications where current direction matters, e.g. the right hand rule or in an electrical circuit. However, that direction is not the direction electrons are flowing even though electrons are the charge carriers in wires. The reasons are mainly historical and have to do with the negative sign assigned to the electrons. The definition of electrical current as being opposite to the electron flow is a complication that confuses a lot of people when they first see current. You should think in terms of current flow and keep in the back of your head the idea that electrons flow in the opposite direction of the current. In circuits, current flows from + to - so in your gadget as shown, if you connect the central wire to the positive side of your power supply, the current will flow from the center out to the brass ring; electrons will flow from the brass ring into the central wire.

 

[Magnetosphere]

Steel disk 5cm diameter. (+) axis, (-) brass ring, power 12 volt car battery 70 amps.