Question

A uniformly charged sphere has a potential on its surface of 460 V. At a radial distance of 32 cm from this surface, the potential is 120 V. What is the radius of the sphere?

Answer 1

Do you know how you would find the potential outside the surface of the sphere if you knew the charge on the sphere? By Gauss's law the E-flux through a sphere bigger than the charged sphere (with the same center) would be proportional to enclosed charge. Because it is uniform, and there is symmetry, the magnitude of the E field would be the same everywhere on the imaginary outer sphere. You can find the E field this way. The potential is the path integral of the E field.

For this problem, though, you don't know what the charge is. However it doesn't matter. If you write out what you know but make the sphere's radius a variable, you can solve it without knowing a charge. You should write down to equations, one for the potential at the unknown radius, and one for the potential at that unknown radius + 32 cm.