Avery long insulating cylinder has radius r and carries positive charge distributed throughout its volume. the charge distribution has cylindrical symmetry but varies with perpendicular distance from the axis of the cylinder. the volume charge density is rho(r)=α(1−r/r), where α is a constant with units c/m^3 and r is the perpendicular distance from the center line of the cylinder.
1. Derive an expression, in terms of α and r, for e(r), the electric field as a function of r.
2. Do this for rr.
3. Do your results agree for r=r?