The magnetic induction outside the magnet can conveniently be expressed as the negative gradient of a magnetostatic potential: . For a point magnetic dipole , . This is integrated over the volume of the magnet. It is most convenient to work in cylindrical coordinates: for the source and , , for the field point ( can arbitrarily be set equal to 0, in view of the anticipated cylindrical symmetry). The detailed computation is given in Details below. A simplifying feature is that integration over shows that the problem can be reduced to two magnetic monopolar disks separated by the distance .

For ease of visualization, only the field lines in the medial plane of the magnet are shown. The three-dimensional field can easily be pictured by virtue of the cylindrical symmetry about the axis. The lines of force originate from the north pole on the right and terminate on the south pole on the left. Magnetic-induction magnitudes are not emphasized in this Demonstration, only the geometry of field lines.