Lag1989 problem number 12.27

An infinitely long cylinder of radius R has a positive charge, the bulk density of which depends only on the distance from its axis according to the law ρ = ρ₀ · (1-r² / R²), where ρ₀ is a constant. Find the field strength E inside and outside the cylinder as a function of the distance from its axis. Dielectric constant ε = 1 inside and outside the cylinder.