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. - AnswerMenu

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.

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(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 km^{2} 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 10^{6} 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? C

To find the max charge, we use the formula for capacitance

The formula for Capacitance is:

C = Q / V (where Q = charge, and V = voltage)

Rearrange, the equation so you are solving for Q.

Q = C*V

Now we just need to find V,

V = E*d (where E = electric field and d = distance )

E = 4 * 10^6 N/C

d = 750 m

V = 4*10^6 N/C * 750 m = 3*10^9 V

Now plug back in the equation for the charge, using C = 1.18 *10^-8 F which was calculated in Part A.

and so

Q = (-1.18*10^-8 F) * (3*10^9 V) = 35.4 C