Let's take an example of magnetic field lines due to a current flowing through a wire. For the sake of the example, assume the wire of infinite length. Now, the magnetic field at any point radial to the wire can be derived. My question is, why are they lines and not a disc area? Why are the iron filings arranged in concentric lines and not a disc with varying thickness, from more thick to less as the distance increases radially?
[Physics] Why are magnetic field lines concentric circles and not a disc
electromagnetismmagnetic fields
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Electromagnetism – If Magnetic Field Lines Don’t Exist, What Do Iron Filings Around a Magnet Show?
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.
why there are gaps between the the iron filling lines?
Iron filings are ferromagnetic. They don't just show the field, they change it.
...hence the iron filings align themselves to stronger field lines.
The filings self-organize into distinct lines because their presence concentrates the field. Magnetic field lines prefer to go through a ferromagnetic body rather than through empty space. The field actually is stronger inside the iron particles than in the gaps between them.
If you drop a new filing into the gap between two of the visible "lines," it will feel attraction toward either of the surrounding lines. It will only stay put, and become the seed for a new line, if the magnetic force that it feels is too weak to overcome the static friction between the particle and the paper (or whatever) underneath.
Best Answer
First, I believe our question is really about how the iron filings are arranged, not about why magnetic field lines are lines. Field lines are abstract concepts which are by definition lines rather than disks (2d objects, or 3d if you allow thickness).
Why does a bunch of iron fillings form a pattern that traces the abstract magnetic field lines, rather than just clustering into a 3d object? This is a nontrivial question.
The answer comes in three conceptual (not chronological) steps. First, the magnetic field magnetizes the iron fillings into a bunch of tiny magnets. Let's just treat each of them as a small round particle. Second, these tiny magnets exert forces on each other. One can show that with some perturbation, the forces prefer them to form a chain with head-to-tail (north-pole-to-south-pole) alignment, rather than a shoulder-to-shoulder configuration. So the powder-like iron filings will form a bunch of tiny needles that are elongated in one direction. Third, each needle behaves like a tiny compass, that points to the direction of the external magnetic field, due to a force known as the magnetic dipolar force. This pattern of needles traces the magnetic field lines.