Estimate the Dielectric Breakdown of Air

[flannabhra]

Homework Statement

A capacitor is charged to V = 5 kV.

A wire is then connected to one plate and is slowly connected to the other. Before actually touching the plate, a spark of length l = 1 cm shoots from the wire to the plate. Using this information, estimate the dielectric breakdown of air, which is the electric field Eair required to generate a spark in air.

Homework Equations

$$E = \frac{V}{d}$$

The Attempt at a Solution

$$E = \frac{V}{d} = 5 * 10^5 \frac{V}{m}$$

 

[rude man]

This is about as good an estimate as you can get.
However, realize that the E field is not constant between the wire and the plate. In fact, the E field at a point like the end of your wire will be very much larger than V/h, so breakdown most probably occurs at and near the wire's tip.

But your estimate is as good as anyone else's, under the circumstances.
.