91Ó°ÊÓ

The magnetic field of Arizona,$B=43\mathrm{μ}\text{T}$

Area of Arizona, $A=2.95×{10}^5{\text{km}}^{\text{2}}$

Use the magnetic flux formula to find the net magnetic flux through the rest of the earth’s surface. The sign of the flux shows its direction. Magnetic flux is a measurement of the total magnetic field which passes through a given area. It is a useful tool for helping describe the effects of the magnetic force on something occupying a given area.

The formula is as follows:

$\mathrm{Ï•}=BA$

where $\mathrm{Ï•}$is the flux,B is the magnetic field, and A is the area.

The magnitude of net magnetic flux through the rest of the Earth’s surface:

Take the negative sign for downward magnetic field and positive sign for the upward magnetic field.

The magnetic flux through Arizona is,

${\mathrm{Ï•}}_B=-BA$

${\mathrm{ϕ}}_B=\left(-43×{10}^{-6}\mathrm{T}\right)\left(2.95×{10}^5{\mathrm{km}}^2\right){\left({10}^3\frac{\mathrm{m}}{\mathrm{km}}\right)}^2$

${\mathrm{ϕ}}_B=-1.3×{10}^7\text{Wb}$

The negative sign shows that this flux goes inward.

Since

role="math" localid="1663146065927" $\begin{array}{rcl}{\mathrm{ϕ}}_{net}& =& 0\\ {\mathrm{ϕ}}_{earth}+{\mathrm{ϕ}}_{arizona}& =& 0\\ {\mathrm{ϕ}}_{earth}& =& -\left({\mathrm{ϕ}}_{arizona}\right)\\ {\mathrm{ϕ}}_{earth}& =& -\left(-1.3×{10}^7\text{Wb}\right)\\ {\mathrm{ϕ}}_{earth}& =& 1.3×{10}^7\text{Wb}\end{array}$

This is the flux that goes through the rest of the earth’s surface.

Therefore, the magnitude of net magnetic flux through the rest of the Earth’s surface is $1.3×{10}^7\text{Wb}$.

The positive sign of the earth’s flux shows that its direction is outward.

Hence, its direction is outward.