Distance to electrical arcing?

Question

can anyone tell about if there is a formula that calulates the minumum distance between two electrically charged probes before they arc to each other. Im using a voltage of 8.5KV and resistivity of air is 4x10^3 ohm.meter right? so there must be a relative answer???

Answer 1

If they are spherical, use 33 kV/cm

8.5KV / 33 kV/cm = 0.25 cm

If they are pointed in any way, it will be a lot lower.

Wikipedia

The dielectric breakdown strength of dry air, at Standard Temperature and Pressure, between spherical electrodes is approximately 33 kV/cm. This is only as a rough guide since the actual breakdown voltage is highly dependent upon the electrode shape and size.

Answer 2

there is the 30 kV/cm number. One thing you need to remember is that is the field strength where air breaks down. if you have parallel plate type geometry you would need about 8.5/30 cm between them. if they you have pointy electrodes the field will be higher. so the distance will be smaller. I have a setup that arcs around 10 kV and it is only spaced by about 1 mm, however it has sharpened electrodes so the field is very high. It is notoriously difficult to calculate the field analytically for all but the simplest geometries. Most people just use a computer code that solves poissons equation and gives you the field (that might be more than you need for this though).