The lower region a thundercloud drifting 30 km above the ear

The lower region a thundercloud, drifting 3.0 km above the earth\'s surface, contains 5.0 C of negative charge. Modeling the bottom of the cloud as a disk of radius of 1.0 km. and modeling the cloud and the earth\'s surface as parallel plates, with the earth-plate charged to -10 C estimate the capacitance of the system, the potential difference between the cloud and the ground, the average strength of he electric field, the energy stored in the system.

Solution

a) Capacitance of system :

C = e0 A / d

A = pi R^2

C = (8.854 x 10^-12 x pi x (1 x 10^3)^2 ) / (3 x 10^3)

C = 9.27 x 10^-9 F

b) Q = CV

10 = (9.27 x 10^-9 ) V

V = 1.08 x 10^9 volt

c) E = V/d =  1.08 x 10^9 / (3 x 10^3) = 3.60 x 10^5 N/C

d) Energy = C V^2 /2

= (9.27 x 10^-9 ) ( 1.08 x 10^9 ) ^2 / 2

= 5.40 x 10^9 J