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I am just generally confused at the mechanism behind electrical arcing.

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closed as unclear what you're asking by John Rennie, Kyle Kanos, stafusa, heather, Jon Custer Oct 27 '17 at 15:26

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Arcing happens when the electric field magnitude is high enough to ionize the molecules in the material. The minimum field that does this is called the dielectric strength of the material. For air, the dielectric strength is about $3\times 10^6\ {\rm V/m}$.

You could achieve breakdown with either a large potential difference across a large distance (as in lightning), or with a fairly modest potential difference across a small distance (as in switch contact arcing).

So, if you had two electrodes separated by air that produced a perfectly uniform field between them, you could create arcing with a $3 \times 10^6$ V difference at a distance of 1 m, or with a 3 V difference at a distance of 1 micron. In practice, arcing would occur at much lower potential difference because the field will concentrate around certain parts of the electrodes.

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