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Capacitance of a Thundercloud. The charge center of a
Chapter 24, Problem 62P(choose chapter or problem)
Capacitance of a Thundercloud. The charge center of a thundercloud, drifting 3.0 km above the earth’s surface, contains 20 C of negative charge. Assuming the charge center has a radius of 1.0 km, and modeling the charge center and the earth’s surface as parallel plates, calculate: (a) the capacitance of the system; (b) the potential difference between charge center and ground; (c) the average strength of the electric field between cloud and ground; (d) the electrical energy stored in the system.
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QUESTION:
Capacitance of a Thundercloud. The charge center of a thundercloud, drifting 3.0 km above the earth’s surface, contains 20 C of negative charge. Assuming the charge center has a radius of 1.0 km, and modeling the charge center and the earth’s surface as parallel plates, calculate: (a) the capacitance of the system; (b) the potential difference between charge center and ground; (c) the average strength of the electric field between cloud and ground; (d) the electrical energy stored in the system.
ANSWER:Introduction First we have to calculate the capacitance considering the earth’s surface and the cloud as parallel plate capacitor. Then we have to calculate the potential difference between charge center and ground. Then we have to calculate the electric field strength. And finally we have to calculate the electrical energy stored in the system. Step 1 The capacitance of a parallel plate capacitor is given by Here A is the surface area and is given by So the capacitance is Now here we have 3 r = 1.0 km = 1.0 × 10 m. 0= 8.85 × 10 12 F/m 3 And d = 3.0 km = 3.0 × 10 m. Hence the capacitance of the earth cloud system is