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

[ "article:topic", "authorname:tatumj" ]

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

$B = \frac{\mu_0}{4 \pi} \frac{p}{r^3}.$

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 $$\mu_0/(4 \pi)$$ times the cube of the radius of the planet. If $$\text{B}$$, $$\mu_0$$ and $$r$$ are expressed respectively in $$\text{T, H m}^{-1}$$ and $$\text{m}$$, the magnetic moment will be in $$\text{N m T}^{-1}$$.