Cyclotron Motion Calculator mechanism

Model scope

The core non-relativistic magnitude formulas are standard after replacing q with |q| and defining velocity as v_perp. The specification needs review because it does not define charge-sign handling, perpendicular-velocity handling, kinetic-energy units/conversion, zero-input validation, or the numerical criterion for the relativistic warning.

• For scalar radius and cyclotron frequency, use |q| rather than signed q: r=m|v_perp|/(|q|B) and f=|q|B/(2πm). The signed charge determines rotation direction, not a negative radius or negative frequency.
• The stated r=mv/(qB) is valid only when v means the component perpendicular to the magnetic field, v_perp. A particle with a velocity component parallel to B follows a helix rather than a purely circular orbit.
• The period output is not explicitly provided; under the non-relativistic convention it should be T=1/f=2πm/(|q|B).
• If kinetic energy is accepted, the required non-relativistic conversion is v=sqrt(2K/m), and this constraint should be explicit. The kinetic-energy input unit is not specified.

Units and conventions

• Mass m is in kilograms.
• Charge q is in coulombs; B is in tesla; velocity is in metres per second; radius is in metres; frequency is in hertz; period is in seconds.
• B denotes the positive magnitude |B| of a uniform magnetic field.
• Velocity is the magnitude of the component perpendicular to B unless the instrument explicitly rejects non-perpendicular input.
• Kinetic energy K must be converted to joules before using v=sqrt(2K/m); 1 eV=1.602e-19 J.
• The test calculations use π=3.1415926536 and the supplied numerical particle constants rather than hidden preset rounding.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "mass_kg": 1.673e-27,
    "charge_C": 1.602e-19,
    "velocity_perpendicular_m_per_s": 1000000,
    "B_T": 1
  },
  "expected_outputs": {
    "radius_m": 0.0104432,
    "cyclotron_frequency_Hz": 15239800,
    "period_s": 6.56165e-8
  },
  "working": "r=m v/(|q|B)=(1.673e-27×1.000e6)/(1.602e-19×1.00)=1.673e-21/1.602e-19=1.04432e-2 m. f=|q|B/(2πm)=1.602e-19/(2×3.1415926536×1.673e-27)=1.602e-19/1.0511769e-26=1.52398e7 Hz. T=1/f=1/(1.52398e7)=6.56165e-8 s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero-charge input creates an undefined radius and period and should be rejected. The non-relativistic-only formulas also produce materially inaccurate results at 0.6c unless the calculator flags or handles the relativistic regime. Signed charge and field conventions can additionally yield negative radius/frequency values that require explicit interpretation.

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