The earth's magnetic field at the equator is approximately 0.4G. Estimate the earth's dipole moment.

Explanation

The equatorial magnetic field is,
`B_(E) = (mu_(0)m)/(4pi r^(3))`
We are given that `B_(E) ~ 0.4 G = 4 xx 10^(-5) T`. For r, we take the radius of the earth `6.4 xx 10^(6)m`. Hence,
`m = (4 xx 10^(-5) xx (6.4 xx 10^(6))^(3))/(mu_(0)//4pi) = 4 xx 10^(2) xx(6.4 xx 10^(6))^(3)(mu_(0)//4pi = 10^(-7))`
`= 1.05 xx 10^(23) Am^(3)`
This is close to the value `8 xx 10^(22) Am^(2)` quoted in geomagnetic texts.