Biot-Savart Field of a Straight Wire Calculator mechanism

Model scope

NEEDS_REVIEW because the exact ambiguity is that the listed inputs provide no wire orientation, current-direction convention, or observation-side geometry, yet the claimed output includes a direction. The surrounding medium is also unspecified, and the requested CODATA μ0 precision/version is not identified. The formula and magnitude calculations pass under the explicit infinite-straight-wire, vacuum/nonmagnetic, SI-unit assumptions.

• B=μ0I/(2πr) is correct for the magnetic-field magnitude of an infinitely long, straight wire in vacuum or an approximately nonmagnetic medium, but the spec says only 'long' while the formula is exact only for an infinite wire.
• The stated inputs (current I and distance r) are insufficient to determine the field direction; wire-axis orientation, observation-side geometry, and current sign/convention are missing.
• The medium is unspecified. In a material medium, μ0 generally must be replaced by μ=μ0μr.
• The μ0 'CODATA' version and precision are unspecified. The test vectors use the conventional μ0=4π×10^-7 N/A^2 approximation, which is not the currently exact SI value.

Units and conventions

• I is measured in amperes (A).
• r is measured in metres (m) after any unit conversion.
• B is reported in tesla (T), using 1 T=1 N/(A·m).
• The vectors assume vacuum or a nonmagnetic medium with μ=μ0.
• The vectors use μ0=4π×10^-7 N/A^2, so μ0/(2π)=2×10^-7 T·m/A.
• For direction examples, the wire is along +z, positive current flows in +z, and the observation point is on the +x side; the right-hand rule then gives +y.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "I": 5,
    "I_unit": "A",
    "r": 0.02,
    "r_unit": "m",
    "wire_axis": "+z",
    "current_direction": "+z",
    "observation_side": "+x"
  },
  "expected_outputs": {
    "B_magnitude_T": 0.00005,
    "direction": "+y"
  },
  "working": "B=(μ0 I)/(2πr)=[(4π×10^-7)(5)]/[2π(0.02)] = (20π×10^-7)/(0.04π) = 500×10^-7 = 5×10^-5 T. By the right-hand rule, +z current viewed from the +x side gives +y field."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The instrument breaks on the exact input r=0 because the formula divides by zero and should return an explicit rejection or undefined result. It is also vulnerable to a factor-of-100 error when a distance is entered without an explicit unit.

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