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

`6.67154* 10^(-9)\ F`

13.009503 C

Step-by-step explanation:

`\epsilon_0` = Permittivity of free space =
`8.85* 10^(-12)\ F/m`

k = Dielectric constant of air
`3* 10^6\ V/m`

Side of plate = 0.7 km

A = Area

d = Distance = 650 m

Capacitance is given by

`C=(\epsilon_0A)/(d)\\\Rightarrow C=(8.85* 10^(-12)* 700^2)/(650)\\\Rightarrow C=6.67154* 10^(-9)\ F`

The capacitance is
`6.67154* 10^(-9)\ F`

Electric field is given by

`Q=CV\\\Rightarrow Q=Ckd\\\Rightarrow Q=6.67154* 10^(-9)* 3* 10^6* 650\\\Rightarrow Q=13.009503\ C`

The charge on the cloud is 13.009503 C