# Why does the breakdown voltage increase when the separation between the electrodes is decreased beyond a particular value?

When I was learning about Paschen's law from Wikipedia, I came across the following statement:

Paschen studied the breakdown voltage of various gases between parallel metal plates as the gas pressure and gap distance were varied:

• With a constant gap length, the voltage necessary to arc across the gap decreased as the pressure was reduced and then increased gradually, exceeding its original value.

• With a constant pressure, the voltage needed to cause an arc reduced as the gap size was reduced but only to a point. As the gap was reduced further, the voltage required to cause an arc began to rise and again exceeded its original value.

The first point was easy to understand intuitively. The conduction of gas in the discharge tube increases at first with decrease in pressure as we'd reduce the rate of recombination of ions. Beyond a certain limit, it increases due to lack of charge carriers.

However, I'm unable to understand the second point in a similar way. When the pressure is fixed, it is said that initially the voltage required for dielectric breakdown of air decreases with decrease in the distance between the two electrodes. This is understandable. But the next statement seems counter-intuitive to me:

As the gap was reduced further, the voltage required to cause an arc began to rise and again exceeded its original value.

I expect that the potential difference for observing an electric arc must decrease with decrease in the gap size. But I don't understand why it must increase beyond a particular separation between the electrodes. It would be helpful if you could explain: Why does the breakdown voltage increase when the separation between the electrodes is decreased beyond a particular value?