Problem 20.32

20.32.
We know that capacitance is given by
$C = \frac{\kappa \epsilon_{0} A}{d}$
$C = \frac{(1.00)(8.85 \times 10^{-12} C^{2})(10^{3}m)^{2}}{(N m^{2})(800 m)}$
$C = 1.1 \times 10^{-8} F ~=~ 11 nF$
The potential between the ground and the cloud is given by
V = Ed
$V = (3 \times 10^{6} N/C)(800 m)$
$V = 2.4 \times 10^{9} V$
So, the maximum change in a cloud is given by
Q = CV
Q = (11.1 nF)(2.4 GV)  =  26.6 C