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When iron filings are sprinkled near a bar magnet, they reveal the "shape" of the magnetic field.

enter image description here(source)

But why do the (needle-shaped?) filings aggregate into chunks with empty space between them rather than simply rotating in place to align with the direction of the magnetic field?

In other words, why the surface density of the iron filings is not uniform?

Sparkler
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  • Related? https://physics.stackexchange.com/q/237712/104696 – Farcher Jul 31 '17 at 04:33
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    The iron filings become magnetized and 'want' to stick together. You can try it! Take a magnet and an iron nail, when you make contact between them the tip of the nail will also become magnetized – Nimrod Morag Jul 31 '17 at 05:09
  • I think this answer addresses your question. – Floris Jul 31 '17 at 13:19
  • @Floris not directly. The missing part is why the magnetized filings "equilibrate" into separated "strokes" rather than remain in a uniform surface coverage. – Sparkler Jul 31 '17 at 13:35
  • Did you read the bit that said " _a metal filing will act as a local "field amplifier": it "pulls the field lines towards it", leading to a concentration of field lines at the tip - and a strong (but very localized) gradient. This gradient means that nearby filing particles will strongly attract each other, and align into the characteristic pattern you are familiar with. _ " – Floris Jul 31 '17 at 14:12
  • @Floris yes, but the same argument is true for all the filings so why aggregate in some places is preferred over other places? – Sparkler Jul 31 '17 at 14:15
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    To some extent that is random. It is like rain drop formation: a drop gets a certain size and starts to grow by "eating" small drops around it. A filing attracts the nearest particle, and their attraction grows stronger; however, at a certain distance that attraction is still very small and there, a second particle can become the nucleus. It's a chaotic (nonlinear) system that finds an equilibrium when all the "unconnected" particles have been connected to a larger cluster. – Floris Jul 31 '17 at 14:25
  • @Floris it also appears that there is a characteristic thickness of the formed "strokes", depending on the field strength. – Sparkler Jul 31 '17 at 14:42
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    Does this answer your question? If magnetic field lines don't exist, what are these iron filings doing around a magnet? – Mindwin Remember Monica Feb 10 '20 at 17:31
  • Note to Close Voters: This question has no answer. Therefore, this one should be closed as a dupe of the one I linked above, even though it is younger. – Mindwin Remember Monica Feb 10 '20 at 17:32
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    @Mindwin: The answers there don't (yet) clearly answer this question, and the accepted answer doesn't even address it. Some other answers vaguely or indirectly answer it while making other points. Floris's comment here looks to me like a far better answer than anything that's been posted on the other question. – Peter Cordes Feb 11 '20 at 06:12
  • Is part of the answer just the general ability to see patterns where none exist? A bit like pareidolia? Looking at the picture, yes there is sort of a classic "field lines" pattern there, but really looking at it, rather than glancing and assuming it's more of a mess than you first think. – Jontia Feb 11 '20 at 10:51
  • @PeterCordes yes it does. the answer by Pieter there addresses it here: Individual iron filings will align their long dimension with the magnetic field. - ergo, close this one. – Mindwin Remember Monica Feb 11 '20 at 12:00
  • @Mindwin: Yes, but why do they clump into "lines" like in this picture? That minimal answer doesn't rule out a uniform distribution of filing positions with only their rotations aligned (but that's very much not what happens). If you shake the paper, IIRC the filings tend to stay clumped into lines, not freely move. There is a real physical effect here. – Peter Cordes Feb 11 '20 at 12:03

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I am going to explicitly plagiarise! From Wikipedia https://en.wikipedia.org/wiki/Iron_filings. I'm leaving it pretty much as-is because it's written better than I would put it.

"Iron filings are very small pieces of iron that look like a light powder. Since iron is a ferromagnetic material, a magnetic field induces each particle to become a tiny bar magnet. The south pole of each particle then attracts the north poles of its neighbors, and this process is repeated over a wide area creates chains of filings parallel to the direction of the magnetic field."

If I were to add to this, to think more about the gaps, I would say it might help to step back and think about adding one filing at a time - like the double slit experiment (cos that always makes things really easy to understand, right! ;).

Wherever we put the first piece, it will line up with the field (because it becomes a bar magnet itself).

But if we've put this filing very near one end of the magnet, the magnetic force is strong - if it is strong enough to overcome friction, the filing will slide along and touch the magnet. Further pieces added to that region will do likewise. But, after lots of them have been added, there is no more room for choice. The layer is one-dimensional, so the new additions cannot get to the main magnet; they have to be satisfied with abutting the existing filings. Eventually, the region ends up entirely full - the dense black regions at either end.

When we add a filing a further away from the ends of the magnet, they still line up with the magnetic field because the magnetic force is strong enough to overcome the local friction involved in spinning. But it is not strong enough though to cause the filing to physically slide over to the magnet. If we add another filing very close to that one, it will feel the first filing's new magnetic force and move to stick to it - N-S-N-S. If we add a third one a little further away, it will be too far to feel the 2 filings and will rotate, but remain where it is. Once you end up with some strings of NSNSNSNSNS's here and NSNSNSN's there, they will reinforce more and more. Further new filings will 'want' to join one of these chains, rather than sit in 'empty' space. So the chains want to grow ever thicker but the spaces want to remain empty.

But at some point, we stop adding filings. And maybe /this/ is the key explanation, then! What if we don't stop but we carry on adding more filings? The next filing will plop into a gap but move and stick to a chain. The one after that will do likewise. And the next, and the next. Gradually, all the space will be used up - and the entire area around the magnet will end up as solidly packed as the area near the ends. It will just be one big, black mass of lined-up filings.

That would not make a very good demonstration of the magnetic field lines, so if my reasoning is right, you only want to have a limited number of filings when making these demonstrations - and similarly, Wooly Willy! ( https://en.wikipedia.org/wiki/Wooly_Willy)

Gordon Panther

Gordon Panther
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The surface density of the filings is more in regions where magnetic field is strong. Further the magnetized filings attract each other, thereby increasing the surface density further in regions of higher magnetic field.

This is also not a large deviation from the expected behavior and might just change with experimental conditions

AbsoluteZero
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Field at the beginning ,is near the magnet is highly localised meaning very high density.As they move away they get spread out what causes the density to decrease.

Now simply consider an example of sun,just outside the surface of sun the temperature is millions of degrees meaning the energy would-be in the order of Peta watt or so per sq.m .But when it reaches the earth it would be around 500-1000 watt per sq.m. In simple consider another example, mark five spots randomly on a balloon that is not inflated. Now start inflating it,as you blow more and more air the points get apart and is proportional to square of radius.

ASTRONO
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