1. What is Cyclotron Frequency?

The cyclotron frequency is the frequency at which a charged particle orbits in a uniform magnetic field. It's a fundamental concept in particle physics and is used in devices like cyclotrons and mass spectrometers.

2. How Does the Calculator Work?

The calculator uses the cyclotron frequency equation:

Where:

• \( q \) — Charge of the particle (Coulombs)
• \( B \) — Magnetic field strength (Tesla)
• \( m \) — Mass of the particle (kilograms)
• \( f \) — Cyclotron frequency (Hertz)

Explanation: The equation shows that the frequency is directly proportional to the charge and magnetic field, and inversely proportional to the mass of the particle.

3. Importance of Cyclotron Frequency

Details: Understanding cyclotron frequency is crucial for designing particle accelerators, mass spectrometers, and understanding charged particle motion in magnetic fields in space and laboratory plasmas.

4. Using the Calculator

Tips: Enter the charge in Coulombs, magnetic field in Tesla, and mass in kilograms. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does the cyclotron frequency depend on particle velocity?
A: No, remarkably, the cyclotron frequency is independent of particle velocity in non-relativistic cases.

Q2: What is the relationship between cyclotron frequency and radius?
A: While frequency remains constant, the orbital radius increases with particle velocity (r = mv/qB).

Q3: How does relativity affect cyclotron frequency?
A: At relativistic speeds, the frequency decreases due to mass increase (relativistic mass).

Q4: What are typical cyclotron frequency values?
A: For electrons in a 1 Tesla field: ~28 GHz. Protons in same field: ~15 MHz (due to higher mass).

Q5: What's the difference between cyclotron and Larmor frequency?
A: They're essentially the same concept, though Larmor frequency sometimes refers specifically to precession frequency in magnetic resonance.