# 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

J | current density (A/m^2) (dimensionless) |

ϵ_{0} | dielectric permittivity (F*m^-1) (dimensionless) |

e | magnitude of the charge of the electron (C) (dimensionless) |

m_{e} | electron mass (kg) (dimensionless) |

V_{a} | anode voltage (V) (dimensionless) |

d | distance separating the cathode and the anode (m) (dimensionless) |