Consider two infinitely long, concentric cylindrical shells. The inner shell has a radius R₁ and carries a uniform surface charge density of σ₁, and the outer shell has a radius R₂ and carries a uniform surface charge density of σ₂.

(a) Use Gauss's law to find the electric field in the regions r < R₁, R₁ < r < R₂, and r > R₂.

(b) What is the ratio of the surface charge densities σ₂/σ₁ and their relative signs if the electric field is zero at r > R₂? What would the electric field between the shells be in this case?

(c) Sketch the electric field lines for the situation in (b) if σ₁ is positive.