Lightning As a crude model for lightning, consider the ground to be one plate of

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 470 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 0.30 km on a side. (Dielectric strength of air is 3.0×106V/m) You may want to review ( pages 712 - 718) .

What is the capacitance of this capacitor?

How much charge can the cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results?

Explanation / Answer

Given that

distance d=470 m

length L=0.3 km=300 m

now we find the capacitance of this capacitor

C=ea/d=8.85*10^-12*3.14*300^2/470=5.3nF

now we find the charge

charge q=E*d*C=3*10^6*470*5.3*10^-9=7.5 C

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