The magnetic dipole moment of the Earth is . (a) Assuming that the origin of this magnetism was a magnetised iron sphere at the centre of the Earth, we have to estimate its radius. (b) We have to find the fraction of the volume of the Earth that this sphere would occupy. The density of the Earth’s inner core is . The magnetic dipole moment of an iron atom is .

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The magnetic dipole moment of the Earth is .

A model for explaining the magnetic dipole moment of the Earth is to assume that there is a magnetised iron sphere at the centre of the Earth. Let the radius of this sphere be R. The magnetic dipole moment of an iron atom is and the density of the Earth’s inner core is .

The number density of iron atoms will therefore be

Here is , is the Avogadro constant, and m is the molar mass of iron.

Therefore,

The radius R of the magnetised iron sphere will therefore be given by the relation

The fraction of the volume of the Earth that this sphere would occupy would be