Question

The magnetic moment of the assumed dipole at the earth's centre is 8.0 × 10²² A m². Calculate the magnetic field B at the geomagnetic poles of the earth. Radius of the earth is 6400 km.

Answer 1

Given:
Magnetic moment of dipole at Earth's centre, M = 8.0 × 10²² Am²
Radius of Earth, d = 6400 km
The geomagnetic pole is at the end of the position (axial) of Earth.
Thus, the magnetic field at the axial point of the dipole $\left(B\right)$ is given by
$$\begin{gathered} B=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathit{2}M}{d^{\mathit{3}}} \\ \Rightarrow B=\frac{{10}^{-7}\times 2\times 8\times {10}^{22}}{{\left(64\right)}^3\times {10}^{15}} \\ \Rightarrow B=6\times {10}^{-5}\mathrm{T}=60\mathrm{\mu T} \end{gathered}$$