Consider two infinitely long, concentric cylindrical shells The inner shell has a radius R 1 and carries a uniform surface charge density of 1 , and the outer shell has a radius R 2 and carries a uniform surface charge density of 2 (a) Use Gauss 's law to find the electric field in the regions r R 1 , R 1 r R 2 , and r R 2 (b) What is the ratio of the surface charge densities 2 1 and their relative signs if the electric field is zero at r R 2 What would the electric field between the shells be in this case (c) Sketch the electric field lines for the situation in (b) if 1 is positive

Question: Consider two infinitely long, concentric cylindrical shells. The inner shell has a radius R 1 and carries a uniform surface charge density of 1

Consider two infinitely long, concentric cylindrical shells. The inner shell has a radius R₁and 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?

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