Final answer:
Each piece of a broken bar magnet will have both a north pole and a south pole because magnetic dipoles always occur in pairs and cannot be separated, even at the atomic level.
Step-by-step explanation:
When a bar magnet is broken in two, each of the two resulting pieces will continue to have a north pole and a south pole. This occurs because magnetic dipoles, which consist of a north pole and a south pole, always occur in pairs. Even if you continue to break or cut the magnet into tinier pieces, each piece will inevitably have both a north and a south pole. This fundamental characteristic of magnets is due to the alignment of domains within the material, and this property remains even at the atomic level with particles like iron atoms maintaining both poles. Consequently, the correct answer to your question is A: Each of the two segments of the original bar magnet will have a north and south pole.