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Poles of a broken magnet

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Hi,

Recently I came across an annular permanent magnet (round magnet with a hole in it) which had fallen and broken in half, effectively forming two horse-shoe magnets. I noticed that the two halves had similar poles:
Code:

|---------- S    S--------
|                        |
|                        |
|                        |
|                        |
|                        |
|---- N        N---------|   

(top view)

Therefore it was impossible to put it back together because the two halves repulsed each other one way, and the way the attracted they didn't fit together anymore because it was - of course - not a perfect cut.

I was wondering whether this is a coincidence. Since these magnets are apparently quite expensive it was a bit unpractical to repeat the experiment, but something tells me that one would get this situation every time although I was unable to explain this theoretically.

Any ideas?

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