A long, solid insulating cylinder of radius R = 1 mm has a uniform volume charge density and a total linear charge density of  Lambda = 3:610^ -9 C/m. The electrostatic potential is zero at the surface. a) At what distance from the surface of the cylinder does the potential equal -90 V? b) If an electron is released from rest at the distance found in part (a), what is its speed just before it impacts the surface? c) What is the volume charge density rho  in C/m^3? [Hint: Consider the total charge in a 1-meter length of the cylinder.] d) Use Gauss's Law to obtain an expression for the electric field E(r) inside the cylinder. [Hint: Employ a cylindrical Gaussian surface of length L and radius r < R.] e) What is the potential (in V) on the axis of the cylinder?