Earth has a magnetic dipole moment of 8.0 × 1022 J/T. (a) What current would have to be produced in a single turn of wire extending around Earth at its geomagnetic equator if we wished to set up such a dipole? Could such an arrangement be used to cancel out Earth's magnetism (b) at points in space well above Earth's surface or (c) on Earth's surface?

Yes this arrangement can be used to cancel out earths magnetic field at points well above the Earth's surface.This is because this current loop acts as a magnetic dipole for point above the earth surface

c

No this arrangement can not be used to cancel out earths magnetic field at points on the Earth's surface .this because on the earth surface it shifts from its behavior as a magnetic dipole

Explanation:

From the question we are told that

The magnetic moment of earth is [tex]M = 8.0*10 ^{22} J/T[/tex]

The radius of earth generally has a value of [tex]R = 6378 *10^3 m[/tex]

Magnetic moment is mathematically given as

[tex]M = IA[/tex]

A is the area of the of the earth(assumption that the earth is circular ) and this evaluated as

[tex]A = \pi R^2[/tex]

Now making [tex]I[/tex] the subject in the above formula

[tex]I = \frac{M}{A}[/tex]

[tex]= \frac{M}{\pi R^2}[/tex]

[tex]= \frac{8.0^10^{22}}{\pi (6378 *10^{3})^2}[/tex]

[tex]= 6.26 *10^8 A[/tex]