Source: https://guthlabs.ai/docs/instruments/parallel-plate-capacitor-field-energy-calculator/
instrument / verified-clean
# Parallel Plate Capacitor Field/Energy Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo
**Tranche**: tranche-5
**Evidence ID**: t5-186
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The instrument concept is valid for an ideal parallel-plate capacitor, but the dielectric treatment and charge-versus-voltage input mode must be specified before release. Correct formulas are ε=ε0εr, C=εA/d, E=V/d=Q/(εA), V=Qd/(εA), and U=½CV²=½QV=Q²/(2C).
### Formula and scope findings
- The dielectric input εr is omitted from E=σ/ε0 and C=ε0A/d. For a homogeneous linear dielectric, use ε=ε0εr, E=σ/(ε0εr), and C=ε0εrA/d.
- The formula E=σ/ε0 is correct only for vacuum or εr=1; with a dielectric, σ must be identified as free plate charge density and the dielectric model must be stated.
- σ is not listed as an input. If charge Q is supplied, the calculator must derive σ=Q/A.
- The specification says charge or voltage but does not define how the calculator distinguishes the two modes, nor what happens if both are supplied and inconsistent.
- The energy formula U=½CV² is valid for an ideal linear capacitor; equivalent forms U=½QV and U=Q²/(2C) should be supported or used for charge-input mode.
### Unit assumptions
- Use SI units internally: A in m², d in m, Q in C, V in volts, E in V/m, C in farads, and U in joules.
- Use ε=ε0εr, with ε0=8.8541878128×10^-12 F/m and dimensionless εr.
- The dielectric is homogeneous, linear, isotropic, and fully fills the region between the plates.
- For E=Q/(εA), Q means the magnitude of free charge on one plate; the field is the ideal uniform field between the plates.
- The supplied common-dielectric εr table must specify conditions such as temperature and frequency because dielectric constants can vary.
## Boundary hardening
### Recorded hazards
- Reject or clearly report invalid inputs A≤0, d≤0, or εr≤0; d=0 causes division by zero.
- If Q is used to calculate V or E, A and C must be nonzero.
- If both Q and V are supplied, validate Q=CV within a defined tolerance; otherwise the result is physically inconsistent.
- A dielectric's breakdown field, plate voltage rating, leakage, frequency dependence, and temperature dependence are not modeled.
- The ideal uniform-field result ignores fringing fields and is inaccurate when d is not small compared with the plate dimensions.
- The field outside the plates and the sign/direction of the field are not represented when only magnitudes are returned.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"A": 0.01,
"d": 0.001,
"epsilon_r": 1,
"V": 100
},
"expected_outputs": {
"E": 100000,
"C": 8.8541878128e-11,
"V": 100,
"Q": 8.8541878128e-9,
"U": 4.4270939064e-7
},
"working": "ε=ε0εr=(8.8541878128×10^-12)(1)=8.8541878128×10^-12 F/m. C=εA/d=(8.8541878128×10^-12)(0.01)/(0.001)=8.8541878128×10^-11 F. E=V/d=100/0.001=1.00×10^5 V/m. Q=CV=(8.8541878128×10^-11)(100)=8.8541878128×10^-9 C. U=½CV²=½(8.8541878128×10^-11)(100²)=4.4270939064×10^-7 J."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche5/tranche5-results.json`