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 lambda.

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, lambda, and constants pi and epsilon_0.

Find the direction of the electric field at any point between the cylinders a distance r from the axis.

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, lambda, and constants pi and epsilon_0.

Find the direction of the electric field at any point outside the outer cylinder a distance r from the axis.

Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.