# Child's Law - related to anode current

## 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}) |

I_{a} | anode current (A) |

S | anode surface inner area (m^{2}) |