Parallel Plate Capacitor Field/Energy Calculator mechanism

Model scope

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).

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

• 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.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json