A sphere of radius R has total charge Q. The volume charge density (C/m³) within the sphere is p(r) = C/r², where C is a constant to be determined. 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.

A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r ≤ R ) is $E\left(r\right)=r^4{E}_{max}/R^4$. Find an expression for the volume charge density ρ(r) inside the ball as a function of r.