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

Explanation

Any point on the magnetic poles of Earth will be on the axial line of the magnet.
`B_(ax) = (mu_0)/(4pi) (2M)/(R^3)`
here , `M = 8 xx 10^22 Am^2 , R = 6,400 km = 64 xx 10^5 m`
` therefore B_(ax) = (10^(-7) xx 2 xx 8 xx 10^22)/((64 xx 10^5)^3)`
` = 6 xx 10^(-5) T`
Any point on the equator will be on the equatorial line of magnet.
`B_(eq) = (mu_0)/(4pi) (M)/(R^3) = (B_(ax))/(2) = 3 xx 10^(-5) T`