Coaxial capacitor.

Homework Statement

Consider a coaxial capacitor. If the inner radius is 5mm, the length is 3 cm, and the voltage rating of the capacitor is 2kV, what is the maximum capacitance if the dielectric between the two conductors is 2.3, and E breakdown is 15MV/m.

Homework Equations

$$E_r = \frac{\rho_s a}{\epsilon_r r}$$
a is the inner radius and r is the radius between the inner and outer conductors at whch we want to find the E field. Since the E field will strongest nearest to the inner conductor, I'm using:
$$E_{r,breakdown} = \frac{\rho_s}{\epsilon_r}$$
This is because I want to find the surface charge density nearest to the inner conductor that will !begin to breakdown the dielectric. I figure we never even want to start to breakdown the dielectric. I hope this makes sense.
$$V = \frac{\rho_s a}{\epsilon_r}[ln(a)-ln(b)]$$
with V = 2k I used this to find b (outer radius)
Finally,
$$C = \frac{2\pi\epsilon_r h}{ln(b/a)}$$

The Attempt at a Solution

I derived all the above equations, and pretty much plugged in numbers, and I'm getting about 1.6 farads which seem wrong.

Actually, thinking about it. I don't see why I can't just use gauss' law to find the enclosed charge (with E = E breakdown) and then divide by 2k

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