The magnetic field of the Earth can be approximated as a dipole magnetic field, with horizontal and vertical components, at a point a distance r from the Earth’s centre, given by

where is the magnetic latitude (latitude measured from the magnetic equator toward the north or south magnetic pole). The magnetic dipole moment is . (a) We have to show that the strength at latitude is given by

(b) We have to show that the inclination of the magnetic field is related to the magnetic latitude by

Solution:             Click For PDF Version

The magnetic field of the Earth can be approximated as a dipole magnetic field, with horizontal and vertical components, at a point a distance r from the Earth’s centre, given by

where is the magnetic latitude (latitude measured from the magnetic equator toward the north or south magnetic pole).

The strength of the magnetic field at the latitude will be given by

The inclination of the magnetic field is defined as

We note that