The inner cylinder of a long, cylindrical capacitor has radius ra and linear charge density + λ. It is surrounded by a coaxial cylindrical conducting shell with inner radius rb and linear charge density - λ (see Fig). (a) What is the energy density in the region between the conductors at a distance r from the axis?
(b) Integrate the energy density calculated in part (a) over the volume between the conductors in a length L of the capacitor to obtain the total electric-field energy per unit length.
(c) Use Eq. (24.9) and the capacitance per unit length calculated in Example 24.4 (Section 24.1) to calculate U/L. Does your result agree with that obtained in part (b)?