A long, straight wire carries a current I. The magnetizing field intensity H is measured at a point P close to the wire. A long, cylindrical iron rod is brought close to the wire so that the point P is at the center of the rod. The value of H at P will :

remains almost constant

By Ampere's Circuital Law, as the the ampere's ring around the point does not contain any enclosed current, the magnetic field intensity at the point will be zero.