Metal sphere in air: Breakdown field strength for air is roughly 3 X 106 N/C. If the electric field is greater than this value, stray free electrons (due to ionization of air molecules by cosmic rays) will be accelerated to high enough energies to trigger a chain reaction, as evident by sparks)
(a) There is a limit to the amount of charge that you can put on a metal sphere in air. If you slightly exceed this limit, explain why the breakdown would occur very near the surface of the sphere, rather than somewhere else.
(b) How much excess charge can you put on a meal sphere of 10 cm radius without causing breakdown in the neighboring air, which would discharge the sphere?
(c) How much excess charge can you put on a meal sphere of only 1 mm radius?
(d) If you are asked to design a lighting rod, which could be mounted on the top of a tall building so as to protect the building from lighting strikes, what shape of the top of your lighting rod should be? Explain your reasoning based on your calculations above.