Your professor estimates that the cloud layer is 750 m above the Earth, and has
ID: 1361647 • Letter: Y
Question
Your professor estimates that the cloud layer is 750 m above the Earth, and has an area of 1 square kilometer.
(a) what is the value of the capacitance? Assume the air to be pure and dry.
(b) Your professor starts thinking about lightning and how the dielectric breakdown of the air is set at 3 megaVolts/meter. What would the charge need to be on the cloud/Earth capacitor to unleash lighting?
(c) If air could be replaced with pure water with a dielectric constant k=80 what would the capacitance be?
(d) If the dielectric breakdown for pure distilled water is 65 megaVolts/m how much charge could be held?
Explanation / Answer
a) C = e0 A / d
A = 1 km^2 = 1 x 10^6 m^2
d = 750 m
C = 8.854 x 10^-8 x 10^6 /750 = 1.18 x 10^-4 F
b) Q = CV and V = E.d
Q = CEd
Q = 1.18 x 10^-4 x 3 x 10^6 x 750 = 265620 C
c) C' = kC = 80 x 1.18 x 10^-4 = 9.44 x 10^-3 F
d) Q = CEd
Q = 9.44 x 10^-3 x 65 x 10^6 x 750 = 4.60 x 10^8 C
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