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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?

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Answer:

[tex]6.67154\times 10^{-9}\ F[/tex]

13.009503 C

Explanation:

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

k = Dielectric constant of air [tex]3\times 10^6\ V/m[/tex]

Side of plate = 0.7 km

A = Area

d = Distance = 650 m

Capacitance is given by

[tex]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[/tex]

The capacitance is [tex]6.67154\times 10^{-9}\ F[/tex]

Electric field is given by

[tex]Q=CV\\\Rightarrow Q=Ckd\\\Rightarrow Q=6.67154\times 10^{-9}\times 3\times 10^6\times 650\\\Rightarrow Q=13.009503\ C[/tex]

The charge on the cloud is 13.009503 C

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