The Charged Sphere

On a metal sphere the charge sits on the outer surface. Outside, the sphere acts like a point charge at its centre:

$$E = k\,\frac{Q}{r^2}\quad (r \ge R)$$

$$V = k\,\frac{Q}{r}\quad (r \ge R)$$

Inside there is no field, so the potential is the same everywhere, the surface's:

E = 0, V = k Q / R (r < R)