A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +a, where a is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +a.
(a) Calculate the electric field in terms of a and the distance r from the axis of the tube for (i) r < a; (ii) a < r < b; (iii) r > b. Show your results in a graph of E as a function of r.
(b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?