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Solved: Capacitance of a Thundercloud. The charge center
Chapter 24, Problem 62P(choose chapter or problem)
Problem 62P
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.
Questions & Answers
QUESTION:
Problem 62P
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 is the surface area and is given by
So the capacitance is
Now here we have
m.
F/m
And m.
Hence the capacitance of the earth cloud system is