1) The field in between north and south pole of horseshoe magnet are straight and parallel.
2) If the wire is passing perpendicular to the paper, the magnetic lines of force are concentric circles, when the current is passed.
3) The direction of field lines due to the wire in upper part coincides with the direction of field lines of horseshoe magnet.
4) The direction of field lines by the wire in lower part is opposite to the direction of field lines of horseshoe magnet.
5) Hence the net field in upper part is strong and in the lower part is weak.
6) Hence a non-uniform field is created around the wire.