Answer
$\Phi^{\prime}=1.3 \times 10^7 \mathrm{~Wb}$.
Work Step by Step
$$
\Phi=-B_r A=-\left\{43 \times 10^{-6} \mathrm{~T}\right\} \mid\left[295,000 \mathrm{~km}^2 \mid\left[10^3 \mathrm{~m} /\left.\mathrm{km}\right|^2=-1.3 \times 10^7 \mathrm{~Wb},\right.\right.
$$
inward. By Gauss' law this is equal to the negative value of the flux $\Phi^{\prime}$ through the rest of the surface of the Earth.
So $\Phi^{\prime}=1.3 \times 10^7 \mathrm{~Wb}$.
