Mastering Physics: A Conducting Shell around a Conducting Rod

Mastering Physics: A Conducting Shell around a Conducting Rod

(Figure 1) An infinitely long conducting cylindrical rod with a positive charge λ per unit length is surrounded by a conducting cylindrical shell (which is also infinitely long) with a charge per unit length of −2λ and radius r_1, as shown in the figure.

Figure 1

Part A

Question: What is E(r), the radial component of the electric field between the rod and cylindrical shell as a function of the distance r from the axis of the cylindrical rod?

Answer: E(r) =  λ/(2πrϵ_0)

Part B

Question: What is σ_inner, the surface charge density (charge per unit area) on the inner surface of the conducting shell?

Answer: σ_inner =  −λ/(2πr_1)

Part C

Question: What is σ_outer, the surface charge density on the outside of the conducting shell? (Recall from the problem statement that the conducting shell has a total charge per unit length given by −2λ.)

Answer: σ_outer =  −λ/(2πr_1)

Part D

Question: What is the radial component of the electric field, E(r), outside the shell?

Answer: E(r) =  −λ/(2πrϵ_0)