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# 17.3: The Magnetic Field on the Equator of a Magnet

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

17.3.1

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.