[UPSC CSE 1997] Electrostatics and Magnetostatics (Q245, 20M)

Using Gauss law find the electric field inside a cylindrical capacitor and hence derive the expression for its capacitance. Find the dielectric constant of the material inside a 50\text{ mm} long capacitor of capacitance 40\ \mu\text{F} having inner conductor of radius 1\text{ mm}, outer conductor of radius 10\text{ mm}. Which of the materials has such a value of the dielectric constant ?