# Capacitance Problem; somewhat solved, but units are off

1. Jul 5, 2008

### clairez93

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

An air-filled spherical capacitor is constructed with inner and outer shell radii of 7.00 and 14.0 cm, respectively. (a) Calculate the capacitance of the device. (b) What potential difference between the spheres results in a charge of 4.00 microC on the capacitor?

2. Relevant equations

C = ab / Ke(b-a)
C = Q/V

3. The attempt at a solution

(a) C = ab/Ke(b-a) = (.07m * .14m) / (8.9875*10^9N*m^2/C^2 * .07m) = 1.558*10^-11
(b) C = Q/V
V = Q/C = (4*10^-6C) / (1.558*10^-11) = 2.56*10^17

Book's Answers: (a) 15.6 pF (b) 256 kV

I'm pretty sure I messed up somewhere with units and converting, as I'm not sure what units I ended up with, and these answers are much bigger than the book answers. I'm not sure where I went wrong though.

2. Jul 5, 2008

### Defennder

Your answer and book's matches for (a). But for (b), there is some calculation error. The working is all right, though.

3. Jul 5, 2008

### clairez93

Ah, I see. I put it back into my calculator and came up with the correct answer. 256739 which is equivalent to 256 kV I think.

4. Jul 5, 2008

### Defennder

Yep that's right.