Source: https://guthlabs.ai/docs/instruments/force-on-a-current-carrying-wire-in-a-field/mechanism/

instrument mechanism / verified-clean

# Force on a Current-Carrying Wire in a Field mechanism

The inspectable method record for Force on a Current-Carrying Wire in a Field, kept separate from implementation and qualification.

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

## Model scope

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.

- 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.

## Units and conventions

- 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.

## Inspectable vector

One of 4 source-bound review vectors:

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

## Failure boundary

**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.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/force-on-a-current-carrying-wire-in-a-field/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/force-on-a-current-carrying-wire-in-a-field/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/force-on-a-current-carrying-wire-in-a-field/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`