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

Question

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 510m to be the other plate. Assume the surface area of the cloud to be the same as the area of a square that is 0.50km on a side. (Dielectric strength of air is 3.0*10^6 V/m ) Will rate if correct, I really appreciate it. 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?

Explanation / Answer

The equation for a parallel plate capacitor is: C = ??*A/d, where ?? is the permittivity, d is the distance between the plates, and A is the area of the plates. C = (??*(0.5km * 0.5km))/(510m) = 4.338nF q = CV V = k*d = (3.0*10^6V/m)*(510m) = 1.53TV (teravolts) q = C*V = (4.338nF)*(1.53TV) = 6637C

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