Suppose that the magnetic field of the Earth were due to a single current moving in a circle of radius 2910 km through the Earth’s molten core. The strength of the Earth’s magnetic field on the surface near a magnetic pole is about 6.0·10–5 T. How large a current (in the equatorial plane) would be required to produce such a field?
You will need the distance from the center of the Earth to the North Pole, which is 6380 km.
Note that in this case the distance to the Pole (the axial distance z) is NOT >> the radius of the current loop, r.