Magnetic Field of a Current Loop / Solenoid Calculator mechanism

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

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