Child–Langmuir law
E371829
The Child–Langmuir law is a fundamental space-charge-limited current law in vacuum electronics that relates the current density between parallel electrodes to the applied voltage raised to the three-halves power.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Child–Langmuir law canonical | 1 |
| non-planar Child–Langmuir law | 1 |
| relativistic Child–Langmuir law | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3583693 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Child–Langmuir law Context triple: [Theory and Design of Electron Beams, topic, Child–Langmuir law]
-
A.
Fick's first law of diffusion
Fick's first law of diffusion is a fundamental physical law that relates the diffusive flux of particles to the spatial gradient of their concentration, describing how substances move from regions of high to low concentration.
-
B.
Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
-
C.
Saha ionization equation
The Saha ionization equation is a fundamental formula in astrophysics and plasma physics that relates the ionization state of a gas in thermal equilibrium to its temperature and pressure, crucial for understanding stellar atmospheres and spectra.
-
D.
Lusser's law
Lusser's law is a reliability engineering principle that states the overall reliability of a system is the product of the reliabilities of its individual components, highlighting how system reliability decreases as more components are added in series.
-
E.
Goodman–Martínez–Thompson correlation
The Goodman–Martínez–Thompson correlation is the most widely accepted scholarly conversion formula that aligns dates in the ancient Maya Long Count calendar with the Gregorian calendar.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Child–Langmuir law Target entity description: The Child–Langmuir law is a fundamental space-charge-limited current law in vacuum electronics that relates the current density between parallel electrodes to the applied voltage raised to the three-halves power.
-
A.
Fick's first law of diffusion
Fick's first law of diffusion is a fundamental physical law that relates the diffusive flux of particles to the spatial gradient of their concentration, describing how substances move from regions of high to low concentration.
-
B.
Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
-
C.
Saha ionization equation
The Saha ionization equation is a fundamental formula in astrophysics and plasma physics that relates the ionization state of a gas in thermal equilibrium to its temperature and pressure, crucial for understanding stellar atmospheres and spectra.
-
D.
Lusser's law
Lusser's law is a reliability engineering principle that states the overall reliability of a system is the product of the reliabilities of its individual components, highlighting how system reliability decreases as more components are added in series.
-
E.
Goodman–Martínez–Thompson correlation
The Goodman–Martínez–Thompson correlation is the most widely accepted scholarly conversion formula that aligns dates in the ancient Maya Long Count calendar with the Gregorian calendar.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
law of vacuum electronics
ⓘ
physical law ⓘ space-charge-limited current law ⓘ |
| alsoKnownAs |
Child law
ⓘ
three-halves power law ⓘ |
| appliesTo |
parallel-plate electrodes
ⓘ
planar diode geometry ⓘ space-charge-limited current ⓘ vacuum diode ⓘ |
| assumes |
collisionless electron flow
ⓘ
non-relativistic electron velocities ⓘ one-dimensional planar geometry ⓘ space-charge-limited emission ⓘ steady-state conditions ⓘ zero initial electron velocity ⓘ |
| constant |
e (electron charge)
ⓘ
m (electron mass) ⓘ ε₀ (vacuum permittivity) ⓘ |
| derivedFrom |
Poisson equation
ⓘ
conservation of energy ⓘ current continuity equation ⓘ |
| expresses | J ∝ V^{3/2} / d^2 ⓘ |
| field |
accelerator physics
ⓘ
electron optics ⓘ plasma physics ⓘ vacuum electronics ⓘ |
| generalizedBy |
Child–Langmuir law
self-linksurface differs
ⓘ
surface form:
non-planar Child–Langmuir law
Child–Langmuir law self-linksurface differs ⓘ
surface form:
relativistic Child–Langmuir law
|
| hasForm | J = (4/9) ε₀ √(2e/m) · V^{3/2} / d^2 ⓘ |
| involves |
electron emission from cathode
ⓘ
space charge ⓘ |
| namedAfter |
Charles D. Child
ⓘ
Irving Langmuir ⓘ |
| relates |
applied voltage
ⓘ
current density ⓘ |
| states | current density is proportional to the three-halves power of the applied voltage ⓘ |
| usedIn |
analysis of field emission limits
ⓘ
analysis of thermionic emission limits ⓘ design of electron guns ⓘ design of high-power microwave devices ⓘ design of klystrons ⓘ design of traveling-wave tubes ⓘ design of vacuum tubes ⓘ ion thruster modeling ⓘ particle accelerator injector design ⓘ plasma sheath theory ⓘ |
| variable |
J (current density)
ⓘ
V (applied voltage) ⓘ d (electrode separation) ⓘ |
| yearProposed | 1911 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Child–Langmuir law Description of subject: The Child–Langmuir law is a fundamental space-charge-limited current law in vacuum electronics that relates the current density between parallel electrodes to the applied voltage raised to the three-halves power.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
relativistic Child–Langmuir law
this entity surface form:
non-planar Child–Langmuir law