By the “equator” of a magnet I mean a plane normal to its magnetic moment vector, passing through the mid-point of the magnet.
The magnetic field at a point at a distance r on the equator of a magnet may be expressed as a series of terms of successively higher powers of 1/r (the first term in the series being a term in r-3), and the higher powers decrease rapidly with increasing distance. At large distances, the higher powers become negligible, so that, at a large distance from a small magnet, the magnitude of the magnetic field produced by the magnet is given approximately by
For example, if the surface magnetic field on the equator of a planet has been measured, and the magnetic properties of the planet are being modelled in terms of a small magnet at the centre of the planet, the dipole moment can be calculated by multiplying the surface equatorial magnetic field by m0/(4p) times the cube of the radius of the planet. If B, m0 and r are expressed respectively in T, H m-1 and m, the magnetic moment will be in N m T-1.