Question

We model the surface of Earth and a cloud layer at 925 m height as a parallel plate capacitor (a) If the clouds cover an area of 3.0 km2, what is the capacitance of our model (in nF)? nF If an electric eld strength exceed g 3,0 × 106 NC causes ightning (the ar becomes conducting what is the maximum charge n C) that can be present on the cloud layer (D (c) Assume the capacitor discharges in a single lightning strike. How much energy is released in the strike (in 3)2

Answer 1

(a) C = E_0 A/d C = 8.8 times 10^minus 12 times 3 times 10^6/925 C = 2.87 times 10^minus 8 F C = 28.7 nF (b) E = Q/E_o A Q = E E_0 A Q = 3 times 10^6 times 8.85 times 10^minus 12 times 3 times 10^6 Q = 79.65 C (c) Energy = Q^2/5C Energy = 79.65^2/2 times 2.87 times 10^minus 9 Energy = 1.105 times 10^11 J