# Capacitance help

1. Feb 6, 2008

### lostfan176

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

k= 9e9
eo = 8.85e-12

3. 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

2. Feb 6, 2008

### foxjwill

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

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

3. Feb 6, 2008

### lostfan176

thanks. i dont know why put my teacher has it like that on his equation sheet

Calculate the charge stored in the "capacitor" = 18.585

Calculate the energy stored in the "capacitor" =

should be 35000000 * 18.585 right?

Last edited: Feb 6, 2008
4. Feb 6, 2008

### foxjwill

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

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

5. Feb 6, 2008

### lostfan176

i will.

to find energy you do w =Vq right?

6. Feb 6, 2008

### foxjwill

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

7. Feb 6, 2008

### lostfan176

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

8. Jan 18, 2012

### ylexot

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.

9. Feb 24, 2012

### lolcat

Bump!

10. Feb 25, 2012

### lolcat

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

Last edited: Feb 25, 2012