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Maximum electric field (Emax) refers to the potential electric energy that can occupy a physical space. "The magnitude of the electric field for which dielectric breakdown occurs in a material is called the dielectric strength of that material," explains Physics for Scientists and Engineers: Regular Version. "The dielectric breakdown [when nonconducting materials become ionized in very high electric fields and become conductors] occurs in air at an electric field strength of Emax = 3 x 106 volts (V) per meter (m).
In other words, we can calculate the maximum voltage a conductor - in this case, air, as in the space between the stun gun contacts - can maintain using the equation Emax = 3 x 106 volts (V) per meter (m).
So, let's calculate the dielectric breakdown of air when contacts are spaced 0.01 m (1 cm) apart.
Emax = 3 x 106 V per 0.01 m
Emax = 3 x 1,000,000 V per 0.01 m
Emax = 3,000,000 V per 0.01 m
Emax = 3,000,000 V x 0.01
When stun gun contacts are placed 1 cm apart, voltage cannot exceed 30,000 V.