The minimum electric field for corona discharge at atmospheric pressure is $3\times10^6\,{\rm V/m}$. How is this calculated?

Question

I saw this number on Wikipedia and other videos, but the calculation part is no where to be seen. Can someone explain how this value is calculated?

Answer 1

With proper measuring instruments, it can be done as follows.

First the setup......

We are going to need two parallel metallic plates (just like a parallel plate capacitor). Then we need to connect a high voltage DC supply across these two plates. The magnitude of voltage should be adjustable and the maximum magnitude of voltage across the plates should be up to a million volts. Next we need to be able to measure the distance between the plates. For getting the required value quickly, we should use smaller distances; from 1mm to 5mm.

Now the procedure.....

First adjust the gap between the plates to a predetermined value say 2 mm. Now start increasing the voltage applied across the parallel plates still there is a spark jumping from positive to negative plate. Note down the magnitude of the voltage at which the spark occurs. Try this at least two to three times to get an accurate reading of of voltage (V) and distance between the plates (d). To ensure accuracy, repeat the same procedure for different distance between the two plates.

For each set of readings, use the formula E = V/d to calculate the electric field exactly at or before the occurrence of spark.

The event of occurrence of spark exhibits dielectric breakdown and the electric field at which this breakdown occurs is the maximum magnitude of electric field that the medium(in this case air) can carry without losing its dielectric property that is its dielectric strength.