Earth has a magnetic dipole moment of $\mathbf{\mu }\mathbf{=}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{22}}\mathbf{J}\mathbf{/}\mathbf{T}$. (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?

Magnetic dipole moment is $\mathrm{\mu }=8\times {10}^{22}\mathrm{J}/\mathrm{T}$.

We use the concept of magnetic dipole moment due to wire. Using the equation, we can find the current through the wire.

Formulae:

$\mathrm{\mu }=\mathrm{NIA}$

Using the equation of magnetic moment,

$\mathrm{\mu }=\mathrm{NIA}$

Rearranging it for current,

$\mathrm{I}=\frac{\mathrm{\mu }}{\mathrm{NA}}$

Here area is $\mathrm{A}={\mathrm{\pi r}}^2$, and N is one.

We can write

$\begin{array}{c}\mathrm{I}=\frac{8\times {10}^{22}}{\left(1\right)\left(3.14\right)\times {(6.378\times {10}^6)}^2}\\ =\frac{8\times {10}^{22}}{1.2773\times {10}^{14}}\\ =6.263\times {10}^8\\ =6.3\times {10}^8\mathrm{A}\end{array}$

In a single turn of wire extending around Earth at its geometric equator, if we wished to set up such a dipole, the current would produce $\mathrm{I}=6.3\times {10}^8\mathrm{A}$.

Yes, because far away from the earth surface, both the magnetic dipole moments are the same. If they are equal and opposite, then the net field will be zero.

No, because magnetic fields of both are notthesame. Therefore, boththefields will not cancel out.