In lightning storms, the potential difference between the earth and the bottom of the thunderclouds can be as high as 35000000 V.The bottoms of the thunderclouds are typically 1500 m above the earth, and can have an area of 110 km^2. Modelling the earth-cloud system as a huge capacitor,calculate
a)the capacitence of the earth -cloud system,
b)the charge stored in the capacitor and
c)the energy stored in the capacitor.
a) C = epsilon*A/d = 0.65*10^-6 F
b) Q = CV = 22.7 coulombs
c) E = (1/2) C V^2 = 400*10^6 J
A is the cloud base area, 110*10^6 m^2
d = 1500 m "plate separation"
epsilon = 8.85*10^-12 Farad/m
Check my numbers
To calculate the capacitance of the earth-cloud system, we use the equation:
C = Q / V
where C is the capacitance, Q is the charge stored in the system, and V is the potential difference between the earth and the bottom of the thunderclouds.
a) To find the capacitance (C), we need to calculate the charge (Q) first.
Given:
Potential difference (V) = 35000000 V
To calculate the charge (Q), we need to find the value of Q in terms of coulombs (C).
We can use the formula for the capacitance of a parallel plate capacitor:
C = ε₀ * A / d
where ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.
Let's convert the given values:
Area (A) = 110 km² = 110 × (1000 m)² = 110 × 10⁶ m²
Distance (d) = 1500 m
Now, we need to calculate the permittivity of free space (ε₀).
ε₀ = 8.854 × 10⁻¹² F/m (approximate value)
Substituting the values into the formula, we can solve for Q:
Q = C * V
Q = (ε₀ * A / d) * V
b) Now that we have the value of Q, we can calculate the charge stored in the capacitor.
c) Finally, we can calculate the energy stored in the capacitor using the formula:
E = 0.5 * C * V²