Question

if i cut a magnet in half what happens to its field

Answer 1

It becomes divides into two poles (North and South)

Answer 2

If you cut the magnet length wise it will become two magnets. If you separate the pieces it behaves like two independent magnets. The field lines directions follow the same  characteristics. The magnetic field strength will be different from the original magnet. Refer  the following figure. Here the width of the magnet is ignored. To show the magnetic field two points are selected, one the axis of the magnet and other perpendicular to magnet of length 'd'. If magnet length (2l) becomes less, the magnetic field strength also becomes less at these points of measurement.