Peek's law

In physics, Peek's law defines the electric potential gap necessary for triggering a corona discharge between two wires:

e_v is the "visual critical corona voltage" or "corona inception voltage" (CIV), the voltage required to initiate a visible corona discharge between the wires.

m_v is an irregularity factor to account for the condition of the wires. For smooth, polished wires, m_v = 1. For roughened, dirty or weathered wires, 0.98 to 0.93, and for cables, 0.87 to 0.83, namely the surface irregularities result in diminishing the corona threshold voltage.

r is the radius of the wires in cm.

S is the distance between the center of the wires.

g_v is the "visual critical" electric field, and is given by:

δ is the air density factor with respect to SATP (25°C and 76 cmHg):

g₀ is the "disruptive electric field."

c is an empirical dimensional constant.

The values for the last two parameters are usually considered to be about 30-32 kV/cm (in air ^[1]) and 0.301 cm^½ respectively. This latter law can be considered to hold also in different setups, where the corresponding voltage is different due to geometric reasons.

Note: The formula has an unintuitive implication that "if the distance between the wires is half the diameter (the radius) then the voltage needed for discharge is zero. Ln (1) = 0." I conclude that the distance is measured from the center of the wires. Not obvious in the definition of "S". Thank you.

References

• F.W. Peek (1929). Dielectric Phenomena in High Voltage Engineering. McGraw-Hill. 
• High Voltage Engineering Fundamentals, E.Kuffel and WS Zaengl, Pergamon Press, p366