# Estimate the Dielectric Breakdown of Air

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1. May 30, 2015

### flannabhra

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

2. Relevant equations
$$E = \frac{V}{d}$$

3. The attempt at a solution
$$E = \frac{V}{d} = 5 * 10^5 \frac{V}{m}$$

2. May 31, 2015

### 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.
.

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