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
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.