Answer
$5\times10^{15}J$
Work Step by Step
The magnetic energy density is given by equation 21–10.
$$u=\frac{Energy}{Volume}=\frac{1}{2}\frac{B^2}{\mu_o}$$
Solve for the energy. The volume of a thin shell, as we have here, is the surface area of the shell multiplied by its thickness.
$$Energy=(Volume) \frac{1}{2}\frac{B^2}{\mu_o}$$
$$=(4\pi (6.38\times10^6m)^2(10^4m)) \frac{1}{2}\frac{(0.50\times10^{-4}T)^2}{4 \pi \times10^{-7}(T \cdot m)/A)}$$
$$\approx5\times10^{15}J$$