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

instrument mechanism / verified-clean

# Magnetic Field of a Current Loop / Solenoid Calculator mechanism

The inspectable method record for Magnetic Field of a Current Loop / Solenoid Calculator, kept separate from implementation and qualification.

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

## Model scope

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.

- 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.

## Units and conventions

- 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.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "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."
}
````

## Failure boundary

**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.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/magnetic-field-of-a-current-loop-solenoid-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/magnetic-field-of-a-current-loop-solenoid-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/magnetic-field-of-a-current-loop-solenoid-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`