question_answer 14)

The earth's surface has a negative surface charge density of 10–9 C m–2. The potential difference of 400 kV between the top of the atmosphere and the surface results (due to the conductivity of the lower atmosphere) in a current of only 1800 A over the entire globe. If there were no mechanism of sustain atmospheric electric field, how much time (roughly) would be required to neutralize the earth's surface? (This never happen, practice because there is a mechanism to replenish electric charges, namely the continual thunderstorms and lightning in different parts of the globe.) (Radius of earth = 6.37 x 106 m.) 

Answer:

Surface area of earth A = 4r2                 = 4 x 3.14 x 6.37 x 106 x 6.37 x 106                 = 509.64 x 1012 m2                 Charge, Q = (Charge density, ) x (Surface area A)                 = 10?9 x 509.64 x 1012                 = 509.64 x 103 C.                 Time, t =                   = 283 s.