Using the results the problem 514 (Problem 37.29 (RHK)), we have to predict the value of the Earth’s magnetic field (magnitude and inclination) at (a) the magnetic equator; (b) a point at magnetic latitude ; and (c) the north magnetic pole.

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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 . The radius of the Earth is .

(a)

The Earth’s magnetic field at the magnetic equator will be

The inclination of the Earth’s magnetic field at the magnetic equator will be zero.

(b)

The horizontal and the vertical components of the Earth’s magnetic field at a point on its surface at the magnetic latitude will be

The magnitude of the Earth’s magnetic field at the magnetic latitude will be

The angle of inclination is

(c)

The Earth’s magnetic field at the magnetic north pole will be

The inclination of the Earth’s magnetic field at the magnetic north pole will be

.