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 chargeQ. The electric field Ein inside the sphere (r≤R) is radially outward with field strength
Ein=14πϵ0QR3r

Q: a) 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.

Express your answer in terms of the given quantities and appropriate constants.

b) What is the ratio VcenterVsurface?

a: 2/3
b: 2
c: 1/2
d: 3/2
e: 1