Question

what happens when we break two bar magnets?

Answer 1

Each particle and pieces of a bar magnet has the two pole South & the North pole.
If we break the bar magnet we will get two more magnets with south & north pole on each on them.
The small pieces even after being broken will retain their magnetic property.

Answer 2

when they are good magnets, the broken ends will have the polarity opposite to the other ends in the broken pieces.
So 2 magnets will become 4 magnets but each of 1/2 strength of the original magnet.