We can make a simple capacitor model to study lightning with the cloud and groun

Question

We can make a simple capacitor model to study lightning with the cloud and ground as parallel plates, separated by 540 m. Assume the surface area of the cloud to be the same as the area of a square that is 0.40 km on a side. (Dielectric strength of air is 3.0 times 10^6 V/m). What is the capacitance of this ground-cloud capacitor? Express your answer using two significant figures. How much charge can the cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results? Express your answer using two significant figures.

Explanation / Answer

a.) C = Ao /d = 4002 x 8.854187817× 1012 / 540 = 2.623463057 x 10-9 F

b.) maximum potential difference across the plates before breakdown = dielectric strength x distance between the plates

V = 3 x 106 x 540 = 1.62 x 109 volts

Hence the maximum charge Q = VC = 1.62 x109 x 2.623463057 x 10-9 = 4.25 coulombs

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