In lightning storms, the potential difference between the Earth and the bottom o

Question

In lightning storms, the potential difference between the Earth and the bottom of the thunderclouds can be as high as 30,000,000 V. The bottoms of thunderclouds are typically 1500 m above the Earth, and may have an area of 100 km2. Model the Earth-cloud system as a huge capacitor.

(a) Calculate the capacitance of the Earth-cloud system.
For this I got .59 uF (which was correct)

(b) Calculate the charge stored in the "capacitor."
For this I got 17.7e-3 C (incorrect)

(c) Calculate the energy stored in the "capacitor."
For this I got 26.5e4 J (incorrect)

Explanation / Answer

The potential difference between the Earth and the bottom of the thunder clouds is V = 30.0 MV

The bottoms of the thunder clouds are at a distance d =  1500 m

Area A = 100 km^2

          =100 *10^3 m^2

Capcitance of the Earth cloud system is C = 0A / d

                                                               = 8.85 *10^-12 * 100*10^3 m^2 /1500 m

                                                               = 0.59*10^-6F

(i) Charge stored in a capcitor is Q = CV

                                                     = 0.59*10^-6F * 30.0 *10^6V

                                                      = 17.7 C

(ii) Energy stored in a capcitor is U = 1/2 CV^2

= 1/2 * 0.59 *10^-6F * ( 30*10^6)^2

= 2.65*10^8 J

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