Obviously the iron filings can be seen aligning themselves along the virtual magnetic field lines produced by the permanent magnet, the virtual magnetic field line is made of electromagnetic field due to the alignment of electrons in the magnet but why the patterns, why lines? Do these lines have thickness? Are they due to interference pattern?
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1$\begingroup$ Is this your question: physics.stackexchange.com/questions/349464/… ? $\endgroup$– ThomasCommented Feb 10, 2020 at 6:29
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1$\begingroup$ I think this answer nicely helps to clarify why iron filings appear to clump into linear arrangements, as if they were following lines which "don't exist". $\endgroup$– uhohCommented Feb 10, 2020 at 10:40
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1$\begingroup$ As filings in a magn. field become tiny magnets the permanent magnet should attract them towards the poles as there is a gradient of the density of magn. lines wich means a net attraction towards a pole.A considerable ammount of filings remain in place between two poles due to the friction resistence to their movement by the material they are placed on.They make lines because the greatest attraction and so the alignment between filings is in the direction of the field.As it orient them they start connecting with each other like magnets when you put close two opposite poles.............. $\endgroup$– Janko BradvicaCommented Feb 10, 2020 at 12:03
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$\begingroup$ @ThomassupportsMonica that question has no answers. The Q can only be a valid dupe target if it has an A. In fact, I think we should close the other one as a dupe of this. $\endgroup$– Mindwin Remember MonicaCommented Feb 10, 2020 at 17:30
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$\begingroup$ @Mindwin Yes, but I think this question may have been misinterpreted. The other question is clearer even if it doesn't have an answer. None of the answers here provide an answer to that question. I'm asking OP to clarify. $\endgroup$– ThomasCommented Feb 10, 2020 at 17:55
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7 Answers
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Here's a map of the barometric pressure in the United States.
The map contains isobars, which are lines of constant pressure. These are constructed by starting from an arbitrary point, and following the direction where the pressure doesn't change.
Isobars don't "exist", in the sense that there isn't literally a big white line in the sky hovering over New York City at this moment. Isobars aren't made of anything, and whether or not an isobar goes through a point on a map is decided entirely by how the map maker decided to draw them. But they help you visualize pressure, which is very real.
When people say that magnetic field lines don't "exist", they mean they're like isobars: a completely arbitrary visualization tool that doesn't exist outside of diagrams. But like pressure, the magnetic field itself is as real as it gets. Iron filings follow its direction.
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$\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$– tpg2114Commented Feb 13, 2020 at 4:07
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2$\begingroup$ I understood the contour lines representing isobars don't exist and are just indication of regions of constant pressure. But I don't get how this explains accumulation of iron filing in specific regions of space. Using your analogy, does a coloured gas or something like that accumulate only in the contour lines? If so what properties of the medium determine which regions will be occupied/unoccupied by the coloured gas? Thanks. $\endgroup$– VishnuCommented Feb 18, 2020 at 10:56
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Individual iron filings will align their long dimension with the magnetic field. But then they will also feel the induced magnetization in other iron particles nearby, and they will tend to move toward each other till their points touch.
This is what creates the strings of iron particles. When the needles cannot move from their site, one does not get lines. 
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3$\begingroup$ Why do iron filings get accumulated at specific regions forming a pattern? Why not cover the entire region around a magnet? Is this in some way related to van Allen radiation belts where charges are accumulated in the magnetic field due to Earth? $\endgroup$– VishnuCommented Feb 9, 2020 at 10:34
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9$\begingroup$ @GuruVishnu No, in the Van Allen belts there is no interaction between the particles. Iron filings contribute to the field by alignment, by clustering. The particles will move to regions with a strong field and a strong gradient, for example to the tip of a string of other iron particles. $\endgroup$– user137289Commented Feb 9, 2020 at 10:49
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$\begingroup$ Hi your answer helps me a lot but can I ask if an electron magnetic dipole moment could produce this phenomenon or they can't since electron doesn't have domains? $\endgroup$– user6760Commented Feb 9, 2020 at 11:50
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$\begingroup$ @user6760 You are the OP so this is about the iron filings, not about free electrons in space. Iron particles interact with each other by the dipole fields of their magnetizations. Each filing will typically contain a number of domains. Those internal domain walls move in response to the external field which gives an increase in their magnetic moment. And then the particle may move (if there is friction as when they lie on paper) or they will move when in a fluid. $\endgroup$– user137289Commented Feb 9, 2020 at 12:09
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5$\begingroup$ This is the right answer (for me at least). $\endgroup$– uhohCommented Feb 10, 2020 at 10:41
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That does look like there are real lines, doesn't it?
It's because each iron filing becomes its own magnet which affects the others.
Notice how they're all crowded together close to the ends of the magnet, and then there's a region where they're thin, and then they get closer together farther away?
I think that's because close up, the magnetic field of the bar magnet is very strong and is the most important thing. But a little distance from there, the iron filings are each strong magnets and they repel each other to the sides while they strongly attract each other at their ends. If you could cut the bar magnet in half the long way without making enough heat to destroy its magnetic fields, the halves would spring apart because they repel each other. The metal magnet holds itself together too strongly to let that happen. But if you cut it in half the short way, the two halves would cling to each other.
Farther away the iron filing magnets are weaker and so they don't repel each other as much and the lines get closer.
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3$\begingroup$ I think this is the best answer at explaining why the "lines" don't actually exist. This explanation shows that the "lines" are an effect of the medium and not a result of the force. The force is a continuous field, of which the effects aren't clearly displayed with the iron filings. $\endgroup$ Commented Feb 11, 2020 at 22:42
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2$\begingroup$ I'd like to know how they got the iron filings to clump into "N" and "S"... $\endgroup$ Commented Feb 11, 2020 at 23:12
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$\begingroup$ Are you suggesting that the "field lines" (vector field, if you want) without the filing has a different shape? $\endgroup$ Commented Feb 12, 2020 at 10:34
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1$\begingroup$ I expect it has generally the same shape, but without the lines. And generally the field isn't strongest where the visible lines are closest together. Except at the very ends of the magnet, where the field IS the strongest. If you look closely at the picture, some lines just peter out and end, and some are braided. These are iron-filing artifacts and don't reflect what the field does when the filings are not there. $\endgroup$– J ThomasCommented Feb 12, 2020 at 15:12
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When we say that magnetic field lines don't exist we mean that there is no physical form of them. Magnetic field lines just represent the direction of force which a ferromagnetic substance like iron would experience in the vicinity of a magnet (the pattern formed by iron filings).
The specific lines or pattern is formed because that the the actual direction of force iron filing would experience when placed freely in the environment
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The iron filings themselves repel each other and create a pattern that can be observed visually as lines.
Liquid metals create mountains that end with peaks as the active forces dissipate, so you can see the concentration is highest nearest the origin.
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2$\begingroup$ Welcome to Physics SE. answers should help to clarify the subject matter of the question. Adding some explication why iron filings repel themselves and clarifying the quite obscure final sentence would make you answer a good answer. $\endgroup$ Commented Feb 10, 2020 at 8:07
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$\begingroup$ This was not very clear but you are probably referring to ferrofluids near a metal. $\endgroup$– user137289Commented Feb 13, 2020 at 9:08
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Magnetic field lines show the direction of force a magnetic mono-pole would experience if it were free to move under the influence of a magnet, but unfortunately, we all know that mono-poles are just a thing of imagination and don't exist in reality. This is given by Gauss' law for magnetism which states
$$\oint \mathbf B\cdot\text d\mathbf s=0$$
Whenever iron filings are scattered around a magnet, they become magnetized and (for a short time) also behave as tiny little magnetic dipoles. Those little magnets can just rotate a bit and align themselves with the field because they can't move and stick to the bar since the experiment table offers some friction.
Now as more of the filings align themselves with the field generated by the adjacent filings, they form a continuous loop around the magnet and that gives us a very nice visual perception of how the magnetic field lines look like. Of course, the "field lines" don't exist in real life.
answered Feb 11, 2020 at 11:15
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1$\begingroup$ "Magnetic field lines show the path a magnetic mono-pole would follow if it were free to move under the influence of a magnet" Not so, for the same reason that a charged particle placed in an $electric$ field won't follow a (curved) electric field line. That's because it acquires a velocity, and its momentum makes it go wide at any bends in the field line. What you need to say is that the $force$ experienced by the particle at any point is always in the direction of the field line through that point. Pedantic? That's what I thought once, but no longer; it pays to be correct. $\endgroup$ Commented Feb 11, 2020 at 11:40
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$\begingroup$ @PhilipWood Thank you so much for telling this. I didn't know that. I'll edit. Unfortunately, some books still use the "path" version. I'm not sure about the advanced books though. $\endgroup$ Commented Feb 11, 2020 at 11:50
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$\begingroup$ I, too have learnt all sorts of things from others' comments on this site. $\endgroup$ Commented Feb 11, 2020 at 18:42
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What is happening when iron filings form a "field line" pattern, is actually an energy minimisation process, somewhat akin to the reason that solar systems form out of rotating clouds of dust. Each individual iron particle becomes magnetised by the applied field, much more so than the surrounding medium. There are then forces acting on the adjacent iron particles which can be treated as lots of small magnets. The minimum energy configuration has the long axis of the particle lined up with the applied field, and particles grouped together into filaments which have roughly the same shape as the imaginary magnetic field lines.
The energy may not be fully minimized -- there is friction with the supporting paper to consider, and also the likelyhood that the pattern gets stuck in a local energy minimum rather than the global one.
You get some truly weird patterns if you use a ferromagnetic liquid and a magnet. (Actually, lots of really tiny more or less spherical ferromagnets suspended in oil).
