Details

The magnetic field can be regarded as originating from two parallel, oppositely charged monopolar disks situated at the ends of the magnet. Since the effective surface magnetic charge densities are equal to , the magnetic field of any point in the - plane, a 2D vector, can be calculated by integrating on those surfaces:

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Mathematica finds a function after integrating with respect to (i.e. in radial direction) that can be written as:

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Snapshot 1: example of field; all vectors go from north pole to south pole

Snapshot 2 : example of field; vectors circulate between north pole and south pole

Snapshot 3 : example of field of thin bar magnet; the field resembles that of two point charges