Source: https://guthlabs.ai/docs/instruments/magnetic-field-of-a-current-loop-solenoid-calculator/

instrument / verified-clean

# Magnetic Field of a Current Loop / Solenoid 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](<https://guthlabs.ai/docs/instruments/magnetic-field-of-a-current-loop-solenoid-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/magnetic-field-of-a-current-loop-solenoid-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/magnetic-field-of-a-current-loop-solenoid-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/magnetic-field-of-a-current-loop-solenoid-calculator/qualification/>)

## 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**: t5-197

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The physics formulas are correct for a single circular loop at its center and an ideal infinite or sufficiently long air-core solenoid. The catalog specification needs review because the role of length is ambiguous and the multi-turn scope of the loop formula is not stated.

### Formula and scope findings

- Both stated formulas are standard under their ideal assumptions: B_loop=μ0I/(2R) gives the field at the center of a single circular loop, and B_solenoid=μ0nI gives the interior field of an ideal long solenoid.

- The input specification is ambiguous: length is listed, but the solenoid formula uses turns density n and does not use length. If n is meant to be calculated from total turns and length, the total number of turns is missing.

- The loop formula does not include a number-of-turns factor; it is valid only for a single-turn loop. A multi-turn loop would require B=μ0NI/(2R), subject to the same-radius approximation.

### Unit assumptions

- Use SI units: current I in amperes, loop radius R in meters, solenoid turns density n in turns per meter, and length in meters.

- Use μ0=4π×10^-7 T·m/A≈1.2566370614359173×10^-6 T·m/A.

- The loop is a single circular loop, and the reported field is at its geometric center.

- The solenoid is air/vacuum-filled and sufficiently long that end effects are neglected; n is turns per meter.

- Solenoid length is not needed when n is supplied directly; if n=N/L is intended, N must be supplied as a separate input.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-radius input creates an undefined division-by-zero result that requires explicit rejection. The specification also leaves geometry-branch selection and current sign/unit conventions implicit, creating risks of silent wrong results.

## 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": {
    "mode": "loop",
    "I": 2,
    "I_unit": "A",
    "R": 0.1,
    "R_unit": "m"
  },
  "expected_outputs": {
    "B": 0.000012566370614359173,
    "B_unit": "T"
  },
  "working": "B=μ0I/(2R)=(1.2566370614359173×10^-6 T·m/A×2 A)/(2×0.1 m)=(2.5132741228718346×10^-6)/(0.2)=1.2566370614359173×10^-5 T."
}
````

## 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`

- `BOUNDARY_HAZARD_CATALOG.json`