# Capacitance Help: Calculating Earth-Cloud System µC

• lostfan176
In summary: OP was asking.In summary, lightning storms can create a potential difference of 35,000,000 V between the Earth and the bottom of thunderclouds. The Earth-cloud system can be modeled as a capacitor with a capacitance of approximately 4779 µC. However, there may be some confusion about the use of the Coulomb constant and kappa in the calculation. It is important to clarify the correct equation and units when solving problems related to capacitors.
lostfan176

## Homework Statement

In lightning storms, the potential difference between the Earth and the bottom of the thunderclouds can be as high as 35,000,000 V. The bottoms of the thunderclouds are typically 1500 m above the Earth, and can have an area of 90 km^2. For the purposes of this problem, model the Earth-cloud system as a huge capacitor. Calculate the capacitance of the Earth-cloud system in µC.

## Homework Equations

C = q/V and C = K eo A/d

k= 9e9
eo = 8.85e-12

## The Attempt at a Solution

9e9 * 8.85e-12 8 (90 000 000 m^2 / 1500) = 4779 C = 4779000000 µC
but this is not right

Why'd you include Coulomb's constant? The equation should be:

$$C=\epsilon_0 \frac{A}{d}$$

thanks. i don't know why put my teacher has it like that on his equation sheetCalculate the charge stored in the "capacitor" = 18.585

Calculate the energy stored in the "capacitor" =

should be 35000000 * 18.585 right?

Last edited:
Point that out to him. It's probably a typo. If it weren't, the equation would simplify to

$$\frac{A}{4\pi d}$$

because

$$k = \frac{1}{4\pi\epsilon_0}$$

i will.

to find energy you do w =Vq right?

Yup. I find it really helpful to check equations by making sure the units on both sides agree.

so the energy of the capacitor should be (35000000 * 18.585) 650475000 J??

For those that are still interested in this post, there seems to be some confusion about the k in the C=κε0A/d equation. This isn't the "Coulomb constant" k = 1/(4π ε0), but rather kappa. Here κ is the dielectric coefficient of the material between the conducting plates. In our cloud example, we're generally talking about the dielectric constant of air.

Bump!

EDIT: Will make a new thread. Realized the question OP posted was different

Last edited:

## 1. What is capacitance and how is it related to the Earth-Cloud system?

Capacitance is the ability of a system to store electrical charge. In the Earth-Cloud system, capacitance refers to the ability of the Earth and the clouds above it to store opposite electrical charges and create an electric field.

## 2. How do you calculate the capacitance of the Earth-Cloud system?

The capacitance of the Earth-Cloud system can be calculated using the formula C = Q/V, where C is capacitance, Q is the charge stored in the system, and V is the potential difference between the Earth and the clouds.

## 3. Can you explain how the charge is distributed in the Earth-Cloud system?

In the Earth-Cloud system, negative charge accumulates on the bottom of the clouds while positive charge accumulates on the surface of the Earth. This creates an electric field between the two, which can result in lightning strikes.

## 4. How does the distance between the Earth and the clouds affect the capacitance of the system?

The capacitance of the Earth-Cloud system is inversely proportional to the distance between the Earth and the clouds. This means that as the distance increases, the capacitance decreases, and vice versa.

## 5. Are there any practical applications of understanding the capacitance of the Earth-Cloud system?

Yes, understanding the capacitance of the Earth-Cloud system is important in predicting and studying lightning strikes. It can also be useful in designing lightning protection systems for buildings and other structures.

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