Question

Answer the following question regarding earth’s magnetism:

The earth’s field, it is claimed, roughly approximates the field due to a dipole of magnetic moment 8 × 10²² J T⁻¹ located at its centre. Check the order of magnitude of this number in some way.

Answer 1

Magnetic moment, M = 8 × 10²² J T⁻¹

Radius of earth, r = 6.4 × 10⁶ m

Magnetic field strength, B = `(μ_0 "M")/(2pi"r"^3)`

Where,

μ₀ = Permeability of free space = 4π × 10⁻⁷ T mA⁻¹

∴ B = `(4pi xx 10^-7 xx 8 xx 10^22)/(4pi xx (6.4 xx 10^6)^3) = 0.3  "G"`

This quantity is of the order of magnitude of the observed field on earth.