Lightning As a crude model for lightning, consider the ground to be one plate of
ID: 1399149 • Letter: L
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 710 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. (Dielectric strength of air is 3.0×106V/m)
A) What is the capacitance of this capacitor?
Express your answer using two significant figures.
B) 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)
Area
A=S2=(0.7*103)2=490,000 m2
Capacitance of the Capacitor
C =eoA/d =(8.85*10-12)*490,000/710
C=6.1*10-9 F or 6.1 nF
b)
Dielectric strength of air
E=3*106 V/m
Potential difference is
V=Ed =3*106*710
V=2.13*109 Volts
Charge on the cloud is
Q=CV =(6.1*10-9)(2.13*109)
Q=13 C
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