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. Calculate the electric field:

a. At any point between the cylinders a distance r from the axis.
b. At any point outside the outer cylinder.
c. Graph the magnitude of the electric field as a function of the distance r from the axis of the cable, from r = 0 to r = 2c.
d. Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.