Peek's law

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

e_v = m_v g_v r \ln \left ({S \over r} \right )

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:

g_v = g_0 \delta \left ( 1 + {c \over \sqrt{\delta r}} \right )

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

\delta = {\rho \over \rho_{SATP}}

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) 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.

References

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

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