# Homework Help: The Earths Capacitance

1. Nov 29, 2012

### lmstaples

1. The problem statement, all variables and given/known data
The earth can be considered as a single-conductor capacitor. It can also be considered in combination with a charged layer of the atmosphere, the ionosphere, as a spherical capacitor with two plates, the surface of the earth being the negative plate. The ionosphere is at a level of about 70km, and the potential difference between earth and ionosphere is about 350000V.

(a) Calculate the capacitance of this system.

(b) Calculate the total charge on the capacitor.

(c) Calculate the energy stored in the system.

2. Relevant equations

$C=\frac{4\pi\epsilon_{0}}{[\frac{1}{R_b}-\frac{1}{R_a}]}$

$Q=CV$

$U=\frac{1}{2}CV^2$

3. The attempt at a solution

Doesn't give me $R_a$ (radius of earth?) so I don't see how to get around it. I assume $R_b - R_a$ is the difference between the radius of earth and the ionosphere, but then I don't know what $R_a R_B$ is.

The rest seems easy once I have the capacitance

2. Nov 29, 2012

### lewando

The mean radius of the Earth is 6371km. It says so on the internet so it is true .