A very long, right circular, cylindrical shell of dielectric constant /0 and inner and outer radii a

Question:

A very long, right circular, cylindrical shell of dielectric constant ε/ε0 and inner and outer radii a and b, respectively, is placed in a previously uniform electric field E0 with its axis perpendicular to the field. The medium inside and outside the cylinder has a dielectric constant of unity.
(a) Determine the potential and electric field in the three regions, neglecting end effects.
(b) Sketch the lines of force for a typical case of b ≈ 2a.
(c) Discuss the limiting forms of your solution appropriate for a solid dielectric cylinder in a uniform field, and a cylindrical cavity in a uniform dielectric.