Lines of Charge: Charge Is Distributed Uniformly Throughout a Large

question 18

Essay

Lines of charge: Charge is distributed uniformly throughout a large insulating cylinder of radius R. The charge per unit length in the cylindrical volume is λ.
(a) Use Gauss's law to find the magnitude of the electric field at a distance r from the central axis of the cylinder for r < R. Your answer should be in terms of r, R, λ, ε₀ , and π.
(b) Check the reasonableness of your answer by evaluating it at the surface of the cylinder.