# Space charge

Space charge is the electrical current that results when a metal object is heated to incandescence in a vacuum.

When a metal object is placed in a vacuum and is heated to incandescence, the energy is sufficient to cause electrons to "boil" away from the surface atoms and surround the metal object in a cloud of free electrons. The resulting cloud is negatively charged, and can be attracted to any nearby positively charged object, thus producing an electrical current which passes through the vacuum.

This effect was first observed by Thomas Edison in light bulb filaments, where it is sometimes called the Edison Effect.

Space charge is an inherent property of all vacuum tubes. This has at times has made life harder or easier for electrical engineers who used tubes in their designs. For example, space charge significantly limited the practical application of triode amplifiers because it impedes the flow of electrons from cathode to anode, thus reducing the level of gain that could be achieved in such tubes.

On the other hand, space charge came in quite handy in some tube applications because it generates a negative EMF within the tube's envelope, which could be utilized to create a negative bias on the tube's grid. This could improve the engineer's control and fidelity of amplification.

Space charges can also occur within a solid, liquid, or gas dielectric. For example, when gas near a high voltage electrode begins to undergo dielectric breakdown, electrical charges are injected into the region near the electrode, forming space charge regions in the surrounding gas. Space charges can also occur within solid or liquid dielectrics that are stressed by high electric fields. Trapped space charges in solid dielectrics is often a contributing factor for dielectric failures within high voltage capacitors and power cables.

## Child's Law

Also known as the Child-Langmuir Law or the Three-Halves Power Law, Child's Law states that the space charge-limited current in a plane-parallel diode varies directly as the three-halves power of the anode voltage and inversely as the square of the distance separating the cathode and the anode.

Mathematically: [itex]I_a=JS=2.33\times10^{-6}\frac{S{V_a}^{3/2}}{d^2}[itex].

This assumes the following:

1. The electrodes are plain, parallel, equipotential surfaces of infinite dimensions.
2. The electrons have zero velocity at the cathode surface.
3. In the interelectrode region, only electrons are present.
4. The current is space-charge limited.
5. The anode voltage remains constant for a sufficiently long time so that the anode current is steady.

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