Insights Are Magnetic Field Lines Real? - Comments

Charles Link

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@Ibix A very interesting article=thank you. :smile: It may be worth mentioning that field lines drawn on a two dimensional piece of paper really don't work very well, because the line density for a source that radiates from a point need to fall off as inverse square, but on a 2-D piece of paper the line density falls off as 1/r. It is a much more accurate representation of actual field lines=they would be quite exact, if they were made out of wire on a 3-D model. Then, the line density would fall off as 1/r^2 away from a point source like they should. ## \\ ## Edit: Note: This is the case with magnetic field lines , where the sources can be considered to be "poles" that obey the inverse square law. (There are also current sources with magnetic fields, but that generally does not complicate matters in regard to the flux lines). In regions where there are no sources, ## \nabla \cdot B=0 ## is obeyed, analogous to the electrostatic ## \nabla \cdot E=0 ##. For both magnetic and electric field lines, the above comments of the 2-D sketch vs. 3-D model apply.
 
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Thanks. @Ibix . There's been some real madness on the forums about this lately, and I think it stems from people taking the iron filling example to mean much more than it actually does.

I do have one question. You said "[f]ield lines are the integral curves of a vector field." Can that sentence be translated into a path integral of some sort?
 

Ibix

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It may be worth mentioning that field lines drawn on a two dimensional piece of paper really don't work very well, because the line density for a source that radiates from a point need to fall off as inverse square, but on a 2-D piece of paper the line density falls off as 1/r. It is a much more accurate representation of actual field lines=they would be quite exact, if they were made out of wire on a 3-D model.
That sounded like a challenge. :wink:
3dField.png

It's a bit of a mess. I think it may need some animation for you to be able to sort out the field lines clearly, but I don't have time right now to figure out how to do that.
 

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Ibix

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Thanks. @Ibix . There's been some real madness on the forums about this lately, and I think it stems from people taking the iron filling example to mean much more than it actually does.
If we're both thinking about the same thread, the problem is something I kind of illustrated with the "bad choices of seed points". You could, indeed, represent the field lines around a moving wire as "moving along with the wire" by picking seed points for the field lines that moved along with the wire - but it's fairly obvious that you are drawing different field lines if you explicitly note that you need to move your seed points. If you used fixed seed points while the wire moves, the field lines just expand. The field lines change over time if the current is changing with time is, I think, the only safe statement of that kind that can be made.
I do have one question. You said "[f]ield lines are the integral curves of a vector field." Can that sentence be translated into a path integral of some sort?
I don't think so, although I'm open to correction. My understanding is that a path integral of some (not necessarily vector) field is its integral along a chosen path, while integral curves require the field to have a notion of direction and they let the field define the path. So if you walk through a rainstorm, how wet you get depends on the integral of the flow rate along the path you choose to walk - that's a path integral. But there's no sense of direction in a rainstorm, unless we go and look at the velocity field of the drops. Integral curves of that field would be the paths traced out by the drops as they fall.

Hope that makes sense.
 

Ibix

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I think it may need some animation for you to be able to sort out the field lines clearly, but I don't have time right now to figure out how to do that.
Or a stereogram. If you can kind of cross your eyes until the red wire loops overlap you get a kind of lame 3d effect.
3dField_2.png
 

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If we're both thinking about the same thread, the problem is something I kind of illustrated with the "bad choices of seed points".
Be sure to link to your Insight in that thread :smile:
 

Charles Link

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That sounded like a challenge. :wink:
View attachment 234989
It's a bit of a mess. I think it may need some animation for you to be able to sort out the field lines clearly, but I don't have time right now to figure out how to do that.
@Ibix I would say at least partly successful. It might work better for a cylindrical magnet than it does for a current loop. In any case, it does illustrate the point that the 3-D model is necessary to get the proper divergence of the flux lines, i.e. where density falls off as 1/r^2 from a point source, etc.
 

Ibix

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Ibix

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@Ibix I would say at least partly successful. It might work better for a cylindrical magnet than it does for a current loop. In any case, it does illustrate the point that the 3-D model is necessary to get the proper divergence of the flux lines, i.e. where density falls off as 1/r^2 from a point source, etc.
It's surprisingly non-painful to create a YouTube video. It really needs to be watched in fullscreen mode because the field lines are too fine otherwise.
Half a million "likes" by next Tuesday for this one, you reckon?
 
I do have a question. It's often said as a rule of thumb that the "line density" relates to the strength of the field. However, I don't unterstand the immediate connection between "longer arrows" and "lines closer together", especially since those properties are in some sense "perpendicular" to each other.

Also, can this be seen with iron filings too? I've seen some images that suggest so, others that don't.
 

Ibix

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It's often said as a rule of thumb that the "line density" relates to the strength of the field.
I agree this can only be a rule of thumb, because there are specific counter examples where the contours of magnetic field strength are different shapes from the magnetic field lines (a wire moving perpendicular to its length, for example). And there are cases where the field line density is completely a matter of choice (a stationary wire produces concentric circular field lines - the density is trivially related to the density of seed points).

But there is an element of truth for things like the wire loop (or any permanent magnet). The field lines all pass through the loop (through the magnet), so it makes sense to pick seed points in the finite region where all lines pass. But those lines sweep back around through the infinite outside region and they must space out. I can pick a finite uniformly spaced set of points in the loop, but that cannot correspond to uniform spacing in the infinite region outside - the spacing must grow with distance. So the spacing grows with falling field strength.

So I think it's a rule limited to situations where there's a finite region that all field lines pass through. And it's not independent of the choice of seed points (see the left hand "bad choice of seed point" diagram in the insight). And it's definitely not true in detail. But there's some truth to it.
Also, can this be seen with iron filings too? I've seen some images that suggest so, others that don't
You mean, can you see field lines being more spread out with the iron filings? No, because there is an infinite set of possible field lines. The density effect only works if you pick systematically placed seed points in a finite region where all field lines pass.

However, there are two points to be aware of. First, far from the magnet the field is weak and there's little to drive the self-organisation. So you see fewer lines because there's less strength in the order-imposing process. Secondly, it's not independent of the density of iron filings. If you dump all the filings on top of the magnet so only a few happen to bounce to regions far away, again you won't see many lines. And iron filings are attracted to the magnet, so the density will almost certainly be higher near the magnet unless you're careful to control it. So I'd guess that's why you have this "sometimes you see it, sometimes you don't" feeling. You need to control for filing density variations.
 

anorlunda

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Great Insight, and helpful to dispel misconceptions. :thumbup:

You can expand the article. I think it would be helpful to mention plasmas such as solar prominences where wiki says "the prominence plasma flows along a tangled and twisted structure of magnetic fields generated by the sun’s internal dynamo." Also in the news is magnetic reconnection where the lines twist and cross themselves. Those things don't invalidate what you wrote, but they are a more complicated case where the lines are more than just magnetic, and which can lead laymen to think all magnetic lines are real.
 

Ibix

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Great Insight, and helpful to dispel misconceptions. :thumbup:
Thanks!
You can expand the article.
I don't think I know enough about solar plasma physics to follow your suggestion. I agree it would be a good subject, since I see your point about prominences potentially giving the impression of flowing along field lines. I just don't think I know enough to do it.

If you know of an appropriate source, happy to link it.
 

anorlunda

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I don't think I know enough about solar plasma physics to follow your suggestion.
I don't think you need to explain the plasma, but just mention that you're excluding plasma from the article. BTW, plasma lines cross each other, whereas the kinds of magnetic lines you wrote about can never cross; an important property.
 

Orodruin

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Great insight @Ibix !
 

DrClaude

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Great Insight, but the Wikipedia link is broken :frown:
 

Ibix

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Great Insight, but the Wikipedia link is broken :frown:
That's weird - it works if you "open link in new tab", but not if you just click on it. I tried to link to the page with all the file information instead of the image itself, but maybe Wiki doesn't like that? I'll investigate later.
 

Ibix

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I don't think you need to explain the plasma, but just mention that you're excluding plasma from the article. BTW, plasma lines cross each other, whereas the kinds of magnetic lines you wrote about can never cross; an important property.
Great Insight, but the Wikipedia link is broken :frown:
I believe I've addressed both of these now - added a paragraph on solar flares and linked directly to the image on Wikipedia instead of its details page.
 
Or a stereogram. If you can kind of cross your eyes until the red wire loops overlap you get a kind of lame 3d effect.
View attachment 234991
At first I found it hard to see the 3D shape, even though I have a fair amount of practice viewing this kind of thing. But I realized that I was crossing my eyes inwards rather than outwards. There are two ways of aligning the right and left image, and we need to select the way that the designer intended. Once I lined up my eyes to look behind the screen, I was able to see the lines running through space, including one big loop that seems to arc out of the screen towards you.
 

Ibix

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At first I found it hard to see the 3D shape, even though I have a fair amount of practice viewing this kind of thing. But I realized that I was crossing my eyes inwards rather than outwards.
Interesting. It works for me crossing my eyes inward, and that's the effect I was aiming for. It's possible I messed up creating it, of course! I think the video does the job better, so I shan't try to regenerate it.
 

Orodruin

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Interesting. It works for me crossing my eyes inward, and that's the effect I was aiming for. It's possible I messed up creating it, of course! I think the video does the job better, so I shan't try to regenerate it.
If you do it the other way around I think that should just result in mirroring the dimension going in/out.
 
If you do it the other way around I think that should just result in mirroring the dimension going in/out.
There may be a bit of subjectivity going on here depending on the post-processing in the brain. But when I cross my eyes inward, I am able to lock the two images together pretty easily -- but the fused image seems to have almost no depth.

When I focus beyond the screen, it's more of an effort to get the images to fuse at first, but when I do succeed, it has more depth and realism. There is one loop, just a little clockwise from the upper-right diagonal, that seems to pop right out of the screen and arc through the space between me and the screen. The same loop in the "other version" looks much flatter, as if I'm looking at a 3D scene where a 2D photograph is suspended in the air, perhaps somewhere behind the computer screen.
 
In the original thread "moving-charge-in-a-magnetic-field-problem" the OP was convinced that those magnetic field lines moved along with the source. A few of us tried to convince him that, as the source moved, the field changed in strength at any particular point, but didn't have a "velocity" of it's own. Can you come up with a better way to get this point across?
 

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