6.9 A wire of radius ro is coincident with the axis of a metal cylinder of radius R and length L. The wire is maintained at a positive potential V (statvolts) with respect to the cylinder. The whole system is at some high absolute tem- perature T. As a result, electrons emitted from the hot metals form a dilute gas filling the cylindrical container and in equilibrium with it. The density of these electrons is so low that their mutual electrostatic interaction can be neglected. (a) Use Gauss's theorem to obtain an expression for the electrostatic field which exists at points at a radial distance r from the wire (ro