Question

Lightning As a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and a cloud at an altitude of 650 m to be the other plate. Assume the surface area of the cloud to be the same as the area of a square that is 0.70 km on a side. a. What is the capacitance of this capacitor?b. How much charge can the cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results?

Answer 1

Answer:

$6.67154\times 10^{-9}\ F$

13.009503 C

Explanation:

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

k = Dielectric constant of air $3\times 10^6\ V/m$

Side of plate = 0.7 km

A = Area

d = Distance = 650 m

Capacitance is given by

$C=\dfrac{\epsilon_0A}{d}\\\Rightarrow C=\dfrac{8.85\times 10^{-12}\times 700^2}{650}\\\Rightarrow C=6.67154\times 10^{-9}\ F$

The capacitance is $6.67154\times 10^{-9}\ F$

Electric field is given by

$Q=CV\\\Rightarrow Q=Ckd\\\Rightarrow Q=6.67154\times 10^{-9}\times 3\times 10^6\times 650\\\Rightarrow Q=13.009503\ C$

The charge on the cloud is 13.009503 C