The pole strength of each piece when a bar magnet is cut into two equal halves perpendicular to its length is the same as the pole strength of the original bar magnet. However, the magnetic moment of each piece is half the magnetic moment of the original bar magnet.
In the magnetic pole representation of a material, a magnetic material can be identified as two magnetic poles some distance apart. The magnetic moment of the material is then given by the product of the pole strength and the distance between the poles. When a bar magnet is halved perpendicular to its length, the magnetic moment is halved but the pole strength remains the same. When the magnet is halved lengthwise, the magnetic moment remains the same but the pole strength is halved.