I mean if the magnetic field is slightly increasing or decreasing at a place should'nt there be a gradient of iron filings instead of clear lines? As to me clear lines mean that there is a comparatively strong magnetic area next to a weaker one hence the iron filings are more attracted to that particular area hence forming a line.

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    $\begingroup$ Someone may correct me here, but it seems like this is to do with the iron filings sticking together rather than showing a feature of the magnetic field they're in. $\endgroup$ – Charlie Aug 3 at 12:25

The magnetic field originating from a bar magnet is continuously decreasing when moving away from the bar magnet. It does not have "lines" of stronger field strength. The lines that are forming are a consequence of the magnetic fields generated by the iron fillings themselves.

An iron particle possesses a magnetic moment that aligns with the magnetic field of the bar magnet. The magnetic moment of the particle also generates a magnetic field around it (just as the bar magnet does). Now, two factors of this field are important in the explanation of the lines:

  1. The magnetic field generated by the particle has an opposite direction with respect to the field of the bar magnet (on the sides of the iron particle). Hence, in the region besides the particle, the net field is reduced.
  2. The field generated by the particle (near field) decays faster than the field of the bar magnet (far field). Therefore, after some distance, the reduction of the net field due to the particles is neglectable.

These two arguments combined, explain the iron particle lines. If more particles are added, they will not nest themself in the region besides the already present particles because the field is weaker there. Instead, they will nest themselves somewhat further (in a new line) where the influence of the field of the iron particles is neglectable. As a result, iron particle lines are formed.

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