Potential Problem?

Question

What are (a) the charge and (b) the charge density on the surface of a conducting sphere of radius 0.14 m whose potential is 200 V (with V = 0 at infinity)?

Some work plesae, numbers, equations, etc.

Answer 1

The potential outside the sphere is Q/(4π*e0*r), where e0 is the permittivity of space and r is the radial distance from the sphere center; so the potential at the sphere's radius R is

V = Q/(4π*e0*R)

then the total charge is

Q = 4π*e0*V*R

The charge density is Q divided by the surface area of the sphere, or q = Q/(4π*R), so q = e0*V