Assume that clouds are distributed around the entire earth at a height of `3000 m` above the ground. The atmosphere can be modeled as a spherical capa

Assume that clouds are distributed around the entire earth at a height of `3000 m` above the ground. The atmosphere can be modeled as a spherical capacitor with the earth as one plate and the cloud as other. When the electric field between the earth and the cloud becomes large, the air begins to conduct and the phenomena is called lightning. On a typical day `4 xx 10^(5) C` of positive charge is spread over the surface of the earth and equal amount of negative charge is there on the cloud. Resistivity of the air is `rho = 3 xx 10^(13) Omega m` and radius of the earth `= 6000 km`.
(a) Find the resistance of the air gap between the earth’s surface and cloud.
(b) Estimate the potential difference between the surface of the earth and the cloud
(c) In how much time the capacitor formed between the earth and the cloud will lose 63 % of the charge ?