Source: https://guthlabs.ai/docs/instruments/coulomb-s-law-calculator/mechanism/

instrument mechanism / verified-clean

# Coulomb's Law Calculator mechanism

The inspectable method record for Coulomb's Law Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The physics formula is standard under the stated SI, vacuum, electrostatic, point-charge assumptions, but the specification needs an explicit signed-force convention, a positive-distance constraint, unit handling, and a clear vacuum/point-charge limitation before it can receive PASS.

- The standard magnitude formula is F=|kq1q2|/r²; the supplied F=kq1q2/r² is a signed scalar unless a sign convention is explicitly defined. Direction must be reported separately as repulsive for like signs and attractive for unlike signs.

- The expression k=1/4πε0 requires explicit denominator parentheses: k=1/(4πε0).

- The formula applies to point charges in vacuum or air-like conditions; the specification does not state the medium or point-charge approximation.

## Units and conventions

- q1 and q2 are signed charges in coulombs (C), with microcoulomb and nanocoulomb inputs converted using 1 μC=10^-6 C and 1 nC=10^-9 C.

- r is the positive separation distance in metres (m), with centimetre inputs converted using 1 cm=10^-2 m.

- F is in newtons (N).

- Use vacuum permittivity and k=8.9875517923×10^9 N·m²/C².

- For these vectors, signed F means sign(q1q2) times the force magnitude; positive denotes repulsion and negative denotes attraction.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "q1": 2,
    "q1_unit": "μC",
    "q2": 3,
    "q2_unit": "μC",
    "r": 0.5,
    "r_unit": "m"
  },
  "expected_outputs": {
    "F_N": 0.2157012430152,
    "direction": "repulsive"
  },
  "working": "q1=2×10^-6 C; q2=3×10^-6 C. q1q2=(2×10^-6)(3×10^-6)=6×10^-12 C². r²=(0.5)²=0.25 m². F=8.9875517923×10^9×(6×10^-12)/0.25=8.9875517923×10^9×2.4×10^-11=0.2157012430152 N. Both charges have the same sign, so the force is repulsive."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-separation input produces an undefined result and must be rejected. The specification also leaves unit conversion, signed-versus-magnitude force reporting, and the zero-force direction convention unspecified.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/coulomb-s-law-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/coulomb-s-law-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/coulomb-s-law-calculator/qualification/>)

## 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`

- `BOUNDARY_HAZARD_CATALOG.json`