Force on a Current-Carrying Wire in a Field

Inspectable records

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

t5-209

Ledger rows

1

No ledger note is attached.

Review findings

The listed formulas are valid for total magnetic force on a straight wire segment, not for the claimed force per unit length. The catalog label and output definition must be corrected, or the formula/output must be changed. The honest_label field is n/a even though the current specification has a material scope and units mismatch.

Formula and scope findings

• The stated computation is force per unit length, but F=I(L×B) and F=BILsinθ calculate total force on a straight wire segment, with units of newtons.
• For force per unit length in a uniform field, the correct scalar formula is F/L=IBsinθ, with units of N/m.
• The vector formula should be written as vector F=I(vector L×vector B), where vector L points in the conventional current direction; the listed notation is ambiguous but its intended total-force formula is standard.

Unit assumptions

• I is in amperes (A), L is in meters (m), and B is in teslas (T).
• θ is the angle between the current direction and the magnetic-field vector; the test vectors specify θ in degrees. The implementation must explicitly define degrees versus radians.
• The total-force formula produces newtons (N); the force-per-unit-length formula produces newtons per meter (N/m).
• The formulas assume a straight wire segment in a uniform external magnetic field.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The extreme-magnitude vector overflows ordinary IEEE-754 plain arithmetic: the mathematically finite representation 1×10^924 N becomes Infinity. The instrument should detect and flag this rather than silently returning an unbounded numeric result.

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": {
    "I_A": 5,
    "L_m": 0.4,
    "B_T": 0.3,
    "theta_deg": 90
  },
  "expected_outputs": {
    "F_total_N": 0.6,
    "F_per_length_N_per_m": 1.5
  },
  "working": "sin(90°)=1. F_total = BILsinθ = 0.3×5×0.4×1 = 0.3×2 = 0.6 N. F_per_length = F_total/L = 0.6/0.4 = 1.5 N/m; equivalently IBsinθ = 0.3×5×1 = 1.5 N/m."
}

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