If the Earth,radius 6371 km,was treated as a metallic sphere,and was given 15 kC of excess electric charge,what would the potential be on its surface?

Question

Quizplus · Accepted Answer

The potential $V$ on the surface of a sphere of radius $r$ with charge $Q$ is given by $V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$, where $\epsilon_0$ is the vacuum permittivity ($8.85 \times 10^{-12} \, \text{C}^2/\text{N}\cdot\text{m}^2$). Substituting $Q = 15 \times 10^3 \, \text{C}$ (since 1 kC = 1000 C) and $r = 6371 \times 10^3 \, \text{m}$, we find $V \approx 21 \, \text{MV}$.

If the Earth,radius 6371 Km,was Treated as a Metallic Sphere,and