A sphere of radius R has total charge Q. The volume charge density (C/m³) within the sphere is ρ(r) = C/r², where C is a constant to be determined.
a. The charge within a small volume dV is dq = ρ dV. The integral of ρ dV over the entire volume of the sphere is the total charge Q. Use this fact to determine the constant C in terms of Q and R.

b. Use Gauss’s law to find an expression for the electric field strength E inside the sphere, r ≤ R, in terms of Q and R.
c. Does your expression have the expected value at the surface, r = R? Explain.