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Paschen's Law, named after Friedrich Paschen, dates back to 1889. He studied the breakdown voltage of parallel plates in a gas as a function of pressure and gap distance. The voltage necessary to arc across the gap decreased up to a point as the pressure was reduced. It then increased, gradually exceeding its original value. He also found that decreasing the gap with normal pressure caused the same behavior in the voltage needed to cause an arc.
Using Paschen's Law, the minimum breakdown in air is calculated to be 327 V at standard atmospheric pressure. This occurs at a distance of 7.5 µm.
Below is the “Paschen Curve” for air, two flat parallel copper electrodes, separated by 1 inch, for
pressures between 3x10-2 Torr and 760 Torr. The curves are slightly different for gasses other than air.