Home Light

At what distance, in m, would two parallel plates in a home Light Switch induce an arc?

At what distance, in m, would two parallel plates in a home light switch induce an arc (as they come together on switch closing) if there is a 120 volt difference between the plates?

Given the ideal case:

Let the Dielectric Strength of air be 3MV/m:
Ds = 3*10^6 V/m = constant

If V = 120 V
120 V /x (m) = 3*10^6 V/m
Ideal air breakdown occurs at:
x = 120/(3*10^6) = 0.00004 m = 40 microns

If V = peak = 120*sqr(2) = 170 V
Ideal air breakdown occurs at:
x = 177/(3*10^6) = 0.000059 m = 59 microns

Many factors are being left out here: air humidity, inductive and
capacitive reactance, plate defects, temperature, air pressure,
potential gradient, the actual dielectric constant at closing time,
etc.

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