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(a) Regarding the Earth and a cloud layer 750 m above the Earth as the "plates" of a capacitor,...

Question:

(a) Regarding the Earth and a cloud layer 750 m above the Earth as the "plates" of a capacitor, calculate the capacitance (in nF) of the Earth–cloud layer system. Assume the cloud layer has an area of {eq}1.00 {/eq} km{eq}^2 {/eq} 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 {eq}4.00 \times 10^6 {/eq} N/C throughout the space between them makes the air break down and conduct electricity as a lightning bolt.

(b) What is the maximum charge (in C) the cloud can hold?

The capacitance of a Capacitor:

When considering a parallel plate capacitor, the capacitance is proportional to the area of the plate and is inversely proportional to the distance between the plates. Also, the capacitance is given by the magnitude of the charge on each plate divided by the magnitude of the potential difference between the plates.

Answer and Explanation:

(a) The capacitance of a parallel plate capacitor is

{eq}C=\frac{k \epsilon A}{d}\\ \rm Here:\\ \bullet k(=1.00054)\text{: dielectric constant of...

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Capacitors: Construction, Charging & Discharging

from AP Physics C - Electricity & Magnetism: Exam Prep

Chapter 2 / Lesson 9
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