Dipole model of the Earth's magnetic field

The dipole model of the Earth's magnetic field is a first order approximation of the rather complex true Earth's magnetic field.

Due to effects of the interplanetary magnetic field (IMF), and the solar wind, the dipole model is particularly inaccurate at high L-shells (e.g., above L=3), but may be a good approximation for lower L-shells.

For more precise work, or for any work at higher L-shells, a more accurate model that incorporates solar effects, such as the Tsyganenko magnetic field model, is recommended.

The following equations describe the dipole magnetic field.

is the radial distance from the center of the Earth (using the same units as used for

It is sometimes more convenient to express the magnetic field in terms of magnetic latitude and distance in Earth radii.

is measured northwards from the equator (analogous to geographic latitude) and is related to the colatitude

by In this case, the radial and latitudinal components of the magnetic field (the latter still in the

direction, measured from the axis of the north pole) are given by where

Invariant latitude is a parameter that describes where a particular magnetic field line touches the surface of the Earth.

is the L-shell describing the magnetic field line in question.