# [solved] Average Energy Density of Capacitor

1. Oct 9, 2015

### xSpartanCx

1. The problem statement, all variables and given/known data
An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 48 mm and 72 mm. The electric potential of the inner conductor with respect to the outer conductor is -536 V (k = 1/4πε0 = 8.99 × 109 N · m2/C2) The average energy density of the capacitor is closest to ?

2. Relevant equations
V = 2k(lambda) ln(b/a)
Energy stored = energy density * volume
3. The attempt at a solution
Using the first equation, I was able to determine the charge/length to be 7.3*10^-8 C/m.
So I know the two radii, the voltage, and the charge per length.
However, I can't seem to figure out how to get the length to be able to get either charge or capacitance to be able to plug it into

U = 1/2 qv or U = 1/2 cv^2.

2. Oct 9, 2015

### xSpartanCx

I realized that the L's cancel. So if lambda * L is q, using .5*λL / (2π(.0072-.0048)) = .0013 but that's not the correct answer. What am I doing wrong?

3. Oct 9, 2015

### xSpartanCx

EDIT: I was using the surface area equation and not the volume one.. whoops. I guess I just needed to organize my work more and I was able to figure it out.