Consider a uniformly charged sphere of radius Rand total charge Q. The electric field Eout outsidethe sphere (r≥R) is simply that of a point charge Q. The electric field Ein inside the sphere (r≤R) is radially outward with field strength
Ein=1/4πϵ0(Q/R^3)r

The electric potential Vout outside the sphere is that of a point charge Q. Find an expression for the electric potential Vin at position r inside the sphere. As a reference, let Vin=Vout at the surface of the sphere.

What is the ratio Vcenter/Vsurface?

Graph V versus r for 0≤r≤3R.