Spheres of charge: A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity?

Question

Quizplus · Accepted Answer

The potential $V$ on the surface of a sphere of radius $r$ and charge $Q$ is given by $V = \frac{kQ}{r}$, where $k$ is Coulomb's constant. If the radius is doubled and the charge remains the same, the new potential is $\frac{kQ}{2r}$, which is half the original potential, hence 50 V.

Spheres of Charge: a Conducting Sphere Is Charged Up Such