3. (30 points) Measurements made as early as 1720 showed that there is a downwar

Question

3. (30 points) Measurements made as early as 1720 showed that there is a downward directed electric field at sea level. Subsequent measurements have shown that this electric field (magnitude200 N/C) is uniform all over the surface of the globe. Balloon measurements have shown that the electric field decreases witlh increasing altitude Scientists now model the earth as a spherical capacitor, with the earth and the ionosphere as perfect conductors and the atmosphere in between as a "leaky" insulator @fair eleetric fReld 1S lylesrea. ‘ Positive plate (charges in E2 Negative plate (Farth's surface) Air between plates acts as a resistor 140-km Figure 1 (a) The atmosphere can be modeled s acapacitor, with conductive air between the plates ( We can imagine an equivalent RC circuit for the atmosphere, with theatural discharge of the capacitor in balance with the charging of the capacitor by lightning.

Explanation / Answer

c apacitanc eof a spherical capacitor is given by
C = 4*pi*epsilon(rarb)/(rb - ra)

a. for earth ionospherre system
ra = 6371,000 m
rb = 6421000 m

hence
C = ra*rb/8.98*10^9*(rb - ra)
C = 0.09192851 F

b. given reistance R = 250 ohms
for 90% charge to be neutralised
q = 0.1Q
so
q = Qe^(-t/RC)
0.1 = e^(-t/RC)
t = 52.91 seconds

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