Question

1. You observe (from the safety of a nearby Faraday cage) a storm cloud sitting about 2 miles above an empty field. The field is about 300 meters by 300 meters in area. You seem to recall your physics professor saying that air is a good insulating medium, but that it experiences dielectric breakdown in an electric field whose strength exceeds 3 million Volts per meter. (P1) Estimate how much charge needs to accumulate in the clouds and the field to make a lightning strike inevitable? (P2) Estimate the energy released in such a discharge, assuming that the build up of charge ends up neutralized by the lightning strike.
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Answer 1

we have q= CV
For breakdown to happen , we need 3 * (10^6) V/m
so, 3* (10^6) = Voltage/length = Voltage / ( 2 miles) = Voltage/ (3218.69 m)
so, Voltage = ( 3* (10^6))/ (3218.69) = 932.056209 Volts
Capacitence = A * e0 /d = (300 *300 * 8.854 * (10^-12))/3218.69 = 247.57277 * (10^-12)
so, q = C* V = 247.57277 *(10^-12) * 932.056209 = 0.230751 *(10^-6) Coulumbs.
how much charge needs to accumulate in the clouds and the field to make a lightning strike inevitable = q = 0.230751 *(10^-6) Coulumbs = 0.230751 micro Coulumbs.
2)
energy discharged = 0.5 * C* V^2 = 0.5 * 247.57277 *(10^-12) * 932.056209^2 = 0.10753679 * (10^-3) J = 0.10753679 milli Joules is the answer.