Cyclotron Frequency Calculator
Calculate the frequency of charged particle motion in magnetic fields
Calculate Cyclotron Frequency
Select a particle to auto-fill charge and mass, or choose Custom
Select which parameter you want to calculate. The others will be used as inputs.
Electric charge of the particle
Strength of the uniform magnetic field
Rest mass of the particle
Radius of circular motion (for velocity calculation)
Calculation Results
Formula used: f = qB / (2πm)
Where: f = frequency (Hz), q = charge (C), B = magnetic field (T), m = mass (kg)
This formula assumes non-relativistic motion and uniform magnetic field perpendicular to velocity
Example Calculations
Proton in 1 Tesla Field
Particle: Proton (q = +1e, m = 1.007 u)
Magnetic Field: B = 1.0 T
Calculation: f = (1.602×10⁻¹⁹ × 1.0) / (2π × 1.673×10⁻²⁷)
Cyclotron Frequency: 15.3 MHz
Application: Medical MRI, particle accelerators
Electron in Earth's Magnetic Field
Particle: Electron (q = -1e, m = 0.0005 u)
Magnetic Field: B = 50 μT (Earth's field)
Calculation: f = (1.602×10⁻¹⁹ × 50×10⁻⁶) / (2π × 9.109×10⁻³¹)
Cyclotron Frequency: 1.4 kHz
Application: Van Allen radiation belts, space physics
Common Particles
Electron (e⁻)
q = -1e, m = 0.000549 u
Fundamental lepton
Proton (p⁺)
q = +1e, m = 1.007 u
Hydrogen nucleus
Alpha particle (α)
q = +2e, m = 4.003 u
Helium-4 nucleus
Key Concepts
Lorentz Force
F = q(v × B)
Causes circular motion
Centripetal Force
F = mv²/r
Balances Lorentz force
Relativistic Effects
Important at v ≈ c
Mass increases with speed
Understanding Cyclotron Frequency
What is a Cyclotron?
A cyclotron is a type of particle accelerator that uses a constant magnetic field and an alternating electric field to accelerate charged particles in a spiral path. The particles move in semicircular paths, and the electric field is synchronized with their motion.
Physical Principle
When a charged particle moves in a magnetic field, it experiences a Lorentz force perpendicular to both its velocity and the magnetic field. This force causes the particle to move in a circular path. The frequency of this circular motion is the cyclotron frequency.
Mathematical Derivation
Force balance:
qvB = mv²/r
Angular frequency:
ω = v/r = qB/m
Cyclotron frequency:
f = ω/(2π) = qB/(2πm)
Key Properties
- •Independent of particle velocity (non-relativistic)
- •Proportional to charge-to-mass ratio (q/m)
- •Linear relationship with magnetic field strength