Determine the flux of the electric field through a spherical...

According to Gauss's Law, the total electric flux through a closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space ($\varepsilon_0$).

$\Phi = \dfrac{q_{\text{enclosed}}}{\varepsilon_0}$

The spherical surface has a radius $R$. The charge located at the centre is inside the sphere, while the identical charge positioned at a distance $2R$ from the centre is outside the sphere.

Therefore, the net charge enclosed by the spherical surface is only the charge at the centre.

$q_{\text{enclosed}} = 10^{-7} \text{ C}$

The electric flux through the spherical surface is:

$\Phi = \dfrac{10^{-7}}{8.85 \times 10^{-12}}$

$\Phi \approx 1.129 \times 10^4 \text{ N m}^2 \text{ C}^{-1}$

Rounding to appropriate significant figures, we get:

$\Phi \approx 1.1 \times 10^4 \text{ N m}^2 \text{ C}^{-1}$