Question

If we represent earth’s magnetic field at the equator, by B, the dipole moment of earth (radius = R)’s equivalent magnet is given by

(1) \(\frac{4\pi R^3 B}{μ_0}\) 

(2) \(\frac{4\pi R^2 B}{μ_0}\)

(3) \(\frac{2\pi RB^2}{μ_0}\)

(4) \(\frac{2\pi RB}{μ_0}\)

Answer 1

(1) \(\frac{4\pi R^3 B}{μ_0}\) 

We can assume earths magnetic field as due to a (short) bar magnet, centered at the centre of earth and held along its polar axis. 

We can then write:

where M is the dipole moment of earth’s equivalent magnet.