Charge stored in a capacitor:
Energy stored in a capacitor:
V = 4 × 108 V
d = 10 km = 10000 m
E = V/d = 4 × 108/10000 = 4 × 104 V/m
Storm clouds build up large negative charges, as described in the chapter. The charges dwell in charge centers, regions of concentrated charge. Suppose a cloud has -25 C in a 1.0-km-diameter spherical charge center located 10 km above the ground, as sketched in the figure. The negative charge center attracts a similar amount of positive charge that is spread out on the ground below the cloud.
The charge center and the ground function as a charged capacitor, with a potential difference of approximately 4 x 108 m The large electric field between these two "electrodes" may ionize the air, leading to a conducting path between the cloud and the ground. Charges will flow along this conducting path, causing a discharge of the capacitor - a lightning strike.
1) What is the approximate magnitude of the electric field between the charge center and the ground?
A) 4 x 104 V/m B) 4 x 105 V/m
C) 4 x 106 V/m D) 4 x 107 V/m
2) What is the approximate capacitance of the charge center-ground system?
A) 6 x 10-8 F
B) 2 x 107 F
C) 4 x 106 F
D) 8 x 106 F
3) If the cloud transfers all of its charge to the ground via several rapid lightning flashes lasting a total of 1.90 s, what is the average power?
A) 12.7 GW
B) 3.74 GW
C) 2.74 GW
D) 1.74 GW
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