Chapter 23, Problem 21P

(III) The volume charge density ρ_E within a sphere of radius r₀ is distributed in accordance with the following spherically symmetric relation

${\rho }_{\text{E}}(r)={\rho }_0\left[1-\frac{r^2}{r_0^2}\right]$

where r is measured from the center of the sphere and ρ₀ is a constant. For a point P inside the sphere (r < r₀), determine the electric potential V. Let V = 0 at infinity.