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 the cloud, at an altitude of 550m, to be the other plate. Assume the surface area of the cloud to be the same as the area of a square that is 500m on a side.<BR>a) What is the capacitance of this "capacitor"? (assume air has the same dielectric constant as vacuum)<BR>b) If the electric field strength in the cloud exceeds 3MV/m, there will be a "dielectric breakdown" and charge will flow occur in the form of a lightning flash. What is the potential difference (voltage) between the cloud and the ground at the time of the breakdown?<BR>c) Using the definition of capacitance, determine the charge built up on the cloud at the point of breakdown.<BR>d) If the time it takes for the strike to happen (ie the charge to flow from cloud to ground) is 100

Explanation / Answer

d = 550 m, A = (500 m)^2, a) What is the capacitance of this "capacitor"? (assume air has the same dielectric constant as vacuum) C = e0*A/d, where e0 is epsilon_0 C = 4.023*10^-9 F b) If the electric field strength in the cloud exceeds E = 3MV/m, there will be a "dielectric breakdown" and charge will flow occur in the form of a lightning flash. What is the potential difference (voltage) between the cloud and the ground at the time of the breakdown? V = E*d = 1.65*10^9 V c) Using the definition of capacitance, determine the charge built up on the cloud at the point of breakdown. Q = CV = 6.64 C d) If the time it takes for the strike to happen (ie the charge to flow from cloud to ground) is t = 100 µs, determine the current in this lightning strike. I = Q/t = 6.64*10^4 A

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