A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length λ.
a. Calculate the magnitude of the electric field at any point between the cylinders a distance r from the axis. Express your answer in terms of the variables a, b, c, r, λ and constants π and ϵ 0.
b. Calculate the magnitude of the electric field at any point outside the outer cylinder a distance r from the axis. Express your answer in terms of the variables a, b, c, r, λ and constants π and ϵ 0.
c. Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder. Enter your answers in ascending order separated by a comma.