The Earth's magnetic field is modelled

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Vector calculus and field geometry

The Boundary-Value Problem, Ch The magnetic multipole expansion and the magnetic scalar potential

Problem

The Earth's magnetic field is modelled, to about ten per cent, as a single magnetic dipole of moment m=7.7×1022 A m2m = 7.7\times10^{22}\,\mathrm{A\,m^2} at the centre, with the Earth's radius RE=6.37×106 mR_E = 6.37\times10^6\,\mathrm{m}. Consider a point on the surface at magnetic latitude λ=45∘\lambda = 45^\circ, so that r^\hat{\mathbf r} makes an angle 90∘−λ90^\circ-\lambda with the dipole axis. ((a)) Find the magnitude of the modelled field there. ((b)) Find the dip angle, the angle the field makes with the local horizontal.

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