An air-filled coaxial cable consists of a metal wire of diameter d surrounded by a thin metal sheath of diameter D. When the wire is charged, deduce expressions for the electric field E(r) and electric potential V(r) at a radial distance r (d/2 < r < D/2) from the central axis. Hence deduce the capacitance per unit length of the cable.
The breakdown field strength of air is 3 Mv m-1. If d = 1 mm and D = 1cm, calculate the potential difference between wire and sheath at which electrical breakdown occurs.