(Solution) - The magnetic field of Earth can be approximated as the magnetic -(2025 Original AI-Free Solution)

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The magnetic field of Earth can be approximated as the magnetic field of a dipole. The horizontal and vertical components of this field at any distance r from Earth's center are given by where ? m, is the magnetic latitude (this type of latitude is measured from the geomagnetic equator toward the north or south geomagnetic pole). Assume that Earth's magnetic dipole moment has magnitude ? = 8.00 x 1022 A ? m2.
(a) Show that the magnitude of Earth's field at latitude ? m is given by
(b) Show that the inclination ? i of the magnetic field is related to the magnetic latitude ? m by tan ? i = 2 tan ? m.