⚡ Cyclotron Frequency Calculator
Calculate particle cyclotron frequency in magnetic field
Example: Electron = -1.6 × 10⁻¹⁹ C, Proton = +1.6 × 10⁻¹⁹ C
Example: Earth's field ≈ 5 × 10⁻⁵ T, MRI machine ≈ 1-3 T
Example: Electron = 9.11 × 10⁻³¹ kg, Proton = 1.67 × 10⁻²⁷ kg
How to Use This Calculator
Enter Charge
Input the charge of the particle in Coulombs. Use positive for positive charges (like protons), negative for negative charges (like electrons). The frequency depends on the absolute value of charge.
Enter Magnetic Field
Input the magnitude of the magnetic field in Tesla (T). Use positive values for the magnetic field strength.
Enter Mass
Input the mass of the particle in kilograms. For subatomic particles, use scientific notation (e.g., 9.11e-31 for electron mass).
Calculate
Click the "Calculate Cyclotron Frequency" button to get the frequency in Hertz (Hz). This is the frequency at which the charged particle orbits in the magnetic field.
Formula
f = qB / (2πm)
Where:
- f = Cyclotron Frequency (Hertz, Hz)
- q = Charge (Coulombs, C) - use absolute value
- B = Magnetic Field Strength (Tesla, T)
- m = Particle Mass (kilograms, kg)
- π = Pi (approximately 3.14159)
Example Calculation:
For an electron (q = 1.6 × 10⁻¹⁹ C, m = 9.11 × 10⁻³¹ kg) in a magnetic field of 0.5 T:
f = (1.6 × 10⁻¹⁹) × 0.5 / (2 × π × 9.11 × 10⁻³¹)
f = 8.0 × 10⁻²⁰ / (5.72 × 10⁻³⁰)
f = 1.40 × 10¹⁰ Hz = 14.0 GHz
Note: The cyclotron frequency is independent of the particle's velocity - it depends only on the charge-to-mass ratio and magnetic field strength.
About Cyclotron Frequency Calculator
The Cyclotron Frequency Calculator determines the frequency at which a charged particle moves in a circular path when placed in a uniform magnetic field perpendicular to its velocity. This frequency is independent of the particle's velocity and is fundamental to understanding cyclotrons, particle accelerators, and magnetic confinement systems.
When to Use This Calculator
- Particle Physics: Calculate frequencies in cyclotrons and other particle accelerators
- Plasma Physics: Determine particle motion frequencies in magnetized plasmas
- Mass Spectrometry: Analyze particle frequencies in mass spectrometers
- Magnetic Confinement: Understand particle behavior in magnetic confinement fusion devices
- Educational: Learn about charged particle motion in magnetic fields
Why Use Our Calculator?
- ✅ Precise Calculations: Handles scientific notation for subatomic particles
- ✅ Velocity Independent: Understand that frequency doesn't depend on particle speed
- ✅ Quick Results: Instantly calculate cyclotron frequencies for any particle
- ✅ Free Tool: No registration or payment required
- ✅ Educational: Learn fundamental physics principles
Common Applications
Cyclotrons: Calculate the RF frequency needed to accelerate particles in cyclotron particle accelerators, where particles are synchronized with an alternating electric field that matches their cyclotron frequency.
Mass Spectrometers: Determine how different particles with different mass-to-charge ratios orbit at different frequencies in magnetic fields, enabling separation and identification of particles based on their mass.
Fusion Research: Understand particle motion in tokamaks and other magnetic confinement fusion devices, where charged particles spiral along magnetic field lines at their cyclotron frequency.
Tips for Best Results
- The cyclotron frequency is independent of particle velocity - only depends on q/m ratio and B
- Higher charge or stronger magnetic field increases frequency
- Heavier particles have lower cyclotron frequency
- Use consistent units: charge in Coulombs, magnetic field in Tesla, mass in kg, frequency in Hz
- The frequency determines the radius of the circular path for a given velocity
Frequently Asked Questions
Why is cyclotron frequency independent of velocity?
The magnetic force (qvB) provides centripetal force (mv²/r). Equating these gives r = mv/(qB), and since the period T = 2πr/v = 2πm/(qB), the frequency f = 1/T = qB/(2πm) is indeed independent of velocity. Higher velocity means larger radius, but the same period.
What happens if the magnetic field is not perpendicular to velocity?
If the magnetic field has a component parallel to velocity, the particle will follow a helical path. The cyclotron frequency still applies to the circular component of motion perpendicular to the field.
How is this related to cyclotrons?
Cyclotrons use a fixed-frequency alternating electric field that matches the cyclotron frequency. As particles gain energy and move faster, they move in larger circles but maintain the same orbital frequency, allowing continuous acceleration.
What units should I use?
Use SI units: charge in Coulombs (C), magnetic field in Tesla (T), mass in kilograms (kg), and the result will be in Hertz (Hz). For subatomic particles, use scientific notation.
Can I use this for relativistic particles?
This calculator uses the non-relativistic formula. For particles moving at significant fractions of the speed of light, relativistic corrections are needed, and the frequency becomes velocity-dependent. For most practical cyclotron applications, the classical formula is accurate.
What is the relationship between frequency and radius?
For a given velocity v, the radius is r = mv/(qB). Since frequency f = qB/(2πm) is constant, particles with higher velocities move in larger circles but complete orbits at the same frequency. This is why cyclotrons can continuously accelerate particles.