Consider the Earth and a cloud layer 600 m above the planet to be the plates of a parallel-plate capacitor.
(a) If the cloud layer has an area of 2.0 km2 = 2000000 m2, what is the capacitance?
To determine the capacitance of a parallel-plate capacitor, we can use the formula:
C = ε₀ * (A / d)
Where:
- C is the capacitance
- ε₀ is the permittivity of free space, which is approximately 8.85 x 10^(-12) F/m
- A is the area of one plate
- d is the distance between the plates
In this case, the Earth's surface and the cloud layer form the plates of the capacitor. The cloud layer is situated 600 m above the Earth.
Given:
- A = 2.0 km² = 2.0 * 10^6 m²
- d = 600 m
First, we need to convert the area from square meters to square meters:
A = 2.0 * 10^6 m²
Next, we can substitute the values into the formula to find the capacitance:
C = ε₀ * (A / d)
C = (8.85 x 10^(-12) F/m) * (2.0 * 10^6 m² / 600 m)
Let's calculate the value: