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This is a somewhat tricky question to answer. But you can basically imagine a magnet to be made up of a large amount of "elementary magnets", all of which have a north and a south pole, like this:(N---S) (N---S) (N---S) (N---S)

The combined magnetic field is the combination of each of the individual magnetic field; and since each of those point in the same direction, in this case north to the left, the combined magnetic field will also have north to the left.

If you break the magnet up, you will get smaller pieces, but the "elementary magnets" will still point in the same direction.

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