The magnetic dipole moment of Earth has magnitude 8.00 1022 J/T. Assume that this is produced by charges flowing in Earth’s molten outer core. If the radius of their circular path is 3500 km, calculate the current they produce.

Explanation:

The magnetic dipole moment of a circular coil with a current is given by

where

I is the current in the coil

is the area enclosed by the coil, where

is the radius of the coil

So the magnetic dipole moment can be rewritten as

(1)

Here we can assume that the magnetic dipole moment of Earth is produced by charges flowing in Earth’s molten outer core, so by a current flowing in a circular path of radius

Here we also know that the Earth's magnetic dipole moment is

Therefore, we can re-arrange eq (1) to find the current that the charges produced:

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