(a) Regarding the Earth and a cloud layer 750 m above the Earth as the plates\"
ID: 1882702 • Letter: #
Question
(a) Regarding the Earth and a cloud layer 750 m above the Earth as the plates" of a capacitor, calculate the capacitance of the Earth-cloud layer system. Assume the cloud layer has an area of 1.00 km2 and the air between the cloud and the ground is pure and dry. Assume charge builds up on the cloud and on the ground until a uniform electric field of 4.00 × 106 N/C throughout the space between them makes the air break down and conduct electricity as a lightning bolt. nF (b) What is the maximum charge the cloud can hold?Explanation / Answer
Given
the capacitor of earth and the cloud layer of area A = 1 km^2 = 10^6 m^2
separation of the plates d = 750 m
the electric field is E = 4*10^6 N/C
a)
we know the capacitance of a parallel plate capacitor is
C = epsilon 0*A/d
C = 8.854*10^-12*10^6/750 F
C = 1.1805333333333*10^-8 F
C = 11.80533 nF
b) maximum charge the cloud can hold is
Q = C*V
Q = C*E*d
Q = 11.80533*10^-9*4*10^6 *750 C
Q = 35.41599 C
so the maximum charge the cloud can hold is Q = 35.41599 C
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