Practical demo - Ferromagnetic attraction at interpole boundary

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TL;DR
Experiment with flat side or pointed side of a nail and its attractive forces to an alternating pole static magnet
I was experimenting with multipolar permanent magnets (concentric alternating-polarity) and a nail and noticed something that initially seems counterintuitive.

Using a handheld gauss meter, when scanning normal to the magnet face (z-axis), the measured Bz is maximal near the centre of the magnet (furthest from the alternating pole) and approaches zero at the boundaries between adjacent poles, as expected due to axial cancellation.

However, when placing a small ferromagnetic object (e.g. a steel nail) over the magnet:

• With the flat end facing the magnet, the object consistently snaps to the interpole boundaries, precisely where Bz ≈ 0
• When the nail is flipped and the sharp tip faces the magnet, it preferentially aligns over the centre, where Bz is maximal

Concentric2.webp
Concentric1.webp
Concentric3.webp


This suggests that the attractive force is dominated by field gradients rather than local field magnitude, and that object geometry (flat or point) strongly influences which part of the field is sampled.

Am I correct in interpreting this behaviour as a consequence of ∇(B²) being maximal at the interpole boundaries despite Bz ≈ 0 there? And is the preference of the pointed tip for the centre best explained by flux concentration and field symmetry?

I’m interested in whether there’s a clean way to describe this distinction between measured field strength and force in multipolar permanent magnet geometries.
Thank you.
 

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