The magnetic state of a bar magnet or a horseshoe magnet is extremely complicated.
Because the core current is somewhat symmetrical around the axis of rotation, the associated magnetic field is similar to that of a bar magnet.
Around a bar magnet, for example, the lines of force point from the north pole to the south.
Like a simple bar magnet, this field's primary magnetic flux is directed out from the core in the Southern Hemisphere and down toward the core in the Northern Hemisphere.
The form of the stable geomagnetic field is like that of a bar magnet at the center of the Earth.
If the bar magnet is simply held stationary near the coil, no current is indicated.