Suppose the magnitude of the earth's magnetic field at the magnetic...

The earth's magnetic field can be approximated as a magnetic dipole.

The magnitude of the magnetic field of a short dipole at a distance $r and magnetic latitude$\lambda$is given by:<br><br>$B = \dfrac{\mu_0 M}{4 \pi r^3} \sqrt{1 + 3 \sin^2 \lambda}$<br><br>At the magnetic equator,$\lambda = 0^{\circ}$, so$\sin \lambda = 0$.<br><br>$B_{eq} = \dfrac{\mu_0 M}{4 \pi r^3} = 3.4 \times 10^{-5} \text{ T}$<br><br>At the geomagnetic poles,$\lambda = 90^{\circ}$, so$\sin \lambda = 1$.<br><br>$B_{pole} = \dfrac{\mu_0 M}{4 \pi r^3} \sqrt{1 + 3(1)^2} = 2 \left(\dfrac{\mu_0 M}{4 \pi r^3} \right)

$B_{pole} = 2 B_{eq}$

$B_{pole} = 2 \times 3.4 \times 10^{-5} \text{ T} = 6.8 \times 10^{-5} \text{ T}$