Child's Law - related to anode voltage

Description

First proposed by Clement D. Child in 1911, Child’s law states that the space-charge limited current (SCLC) in a plane-parallel vacuum diode varies directly as the three-halves power of the anode voltage Va and inversely as the square of the distance d separating the cathode and the anode.

For electrons, the current density J (amperes per meter squared) is written as shown here.

Related formulas

Variables

Jcurrent density (A/m^2) (dimensionless)
ϵ0dielectric permittivity (F*m^-1) (dimensionless)
emagnitude of the charge of the electron (C) (dimensionless)
meelectron mass (kg) (dimensionless)
Vaanode voltage (V) (dimensionless)
ddistance separating the cathode and the anode (m) (dimensionless)