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Quiz 4 - Earth Ionosphere Capacitor

As shown in Figure 1, the Earth and the ionosphere (which is a conducting layer at approximately 60 km altitude) form a two conductor spherical capacitor. In a fair weather, an electric field of 10 V/m is found at each point on the surface (r = Re) of the Earth. The field is radial and points toward the center of the Earth. To simplify your calculations, assume Re = 6000 km, εo= 1/36π × 10-9 F/m.

(a) Using Gauss's integral theorem, find the total charge (magnitude and sign) on the Earth's surface.

(b) Lightning is believed to be the source of the charge on the Earth. Assuming each lighting stroke delivers 100 C of charge to the earth, how many lightning strokes are required to charge the Earth? (This gives you the global lightning rate per second, since it takes about one second to charge the Earth).

(c) Once charged, how does the Earth lose this charge?


Solution:

a) Q = 4πEεor2

Q = 4π(10V/m)(1/36π × 10-9 F/m)(6000km)2

Q = -40,000C


b) Q1-stroke = -100C (find number of strokes to charge earth.)
So: It takes approximately 400 strokes / per second to charge the earth


c) The earth looses charge by conducting back into the air. The more moisture content in the air increases the rate that the charge is absorbed.



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