1. Cylindrical Capacitor with Dielectric Let us consider a cylindrical capacitor in which the space between the conductors is filled with an insulating material of dielectric constant k. Assume that the total charges on the outer and inner conductors are +@ and -Q, respectively, and that these charges are uniformly distributed on the conductors' surfaces at r = b and r = a, respectively. The length of the cylindrical capacitor, L, is much greater than the radii a and b so the edge effect can be ignored. (a) What is the electric field between the conductors? (b) Find the potential difference between the "plates" (the conductors) and use it to calcu- late the capacitance. Check that your result agrees with the capacitance of a cylindrical capacitor we found before in class when k = 1. (c) What is the magnitude of the bound charge Q' (the charge on the surfaces of the dielectric due to polarization), in terms of Q and k?(d) The energy density (per unit volume) in an electric field of magnitude E in a dielectric material is 1 = - KEDE:2 Starting with your expression for the electric field between the conducting plates of a cylindrical capacitor, integrate the energy density to find the total energy U in the electric field: U u dv Show that your result agrees with the general expression for energy stored in a capacitor, U = QV 2