Source: https://guthlabs.ai/docs/instruments/cyclotron-motion-calculator/
instrument / verified-clean
# Cyclotron Motion Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## 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**: t5-205
**Ledger rows**: 1
No ledger note is attached.
## Review findings
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.
### Formula and scope findings
- 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.
### Unit assumptions
- 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.
## Boundary hardening
**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.
## 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": {
"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."
}
````
## 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`