Question

The magnetic moment of the assumed dipole at the earth's centre is $8.0\times {10}^{22}A{m}^2$. Calculate the magnetic field B at the geomagnetic poles of the earth. Radius of the earth is 6400 km.

Answer 1

Given that,

the magnetic moment of dipole at earth's centre, $M=8.0\times {10}^{22}A{m}^2$

Radius of earth, $d=6400km$

The geomagnetic pole is at the end on position of the earth.

$B=\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}=\frac{{10}^{-7}\times 2\times 8\times {10}^{23}}{(6400\times {10}^3{)}^3}\approx 60\times {10}^{-6}T=60\mu T$