a) Derive the capacitance per unit length of a coaxial capacitor consisting of a conducting rod, radius a and a conducting tube surrounding it of inner radius b. In your derivation, begin with the definition of capacitance and show all steps.
b) Find the capacitance per unit length of the capacitor if the tube is lined with a sheet of dielectric of thickness t.
c) Assuming the dielectric sheet is thin, evaluate the magnitude of the displacement vector D and the magnitude of the polarisation vector P in the sheet in terms of appropriate variables.