### What is the potential on the axis of the cylinder

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A long, solid insulating cylinder of radius R = 1 mm has a uniform volume charge density and a total linear charge density of  Lambda = 3:610^ -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?

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