1. What is Cyclotron Frequency?

The cyclotron frequency is the frequency at which a charged particle orbits in a uniform magnetic field perpendicular to its motion. It's fundamental in cyclotrons and other particle accelerators.

2. How Does the Calculator Work?

The calculator uses the cyclotron frequency formula:

Where:

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

Explanation: The frequency is independent of the particle's velocity and the radius of its orbit, depending only on the charge-to-mass ratio and magnetic field strength.

3. Importance of Cyclotron Frequency

Details: This frequency is crucial in designing cyclotrons, mass spectrometers, and understanding charged particle motion in magnetic fields in plasma physics and astrophysics.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is cyclotron frequency independent of velocity?
A: While faster particles move in larger circles, they complete orbits at the same rate because the circumference increases proportionally with speed.

Q2: What's a typical cyclotron frequency range?
A: For electrons in a 1 Tesla field, about 28 GHz. For protons in the same field, about 15 MHz (due to their larger mass).

Q3: How does relativistic effects change this?
A: At relativistic speeds, the mass increases (m = γm₀), causing the frequency to decrease as energy increases.

Q4: What's the difference between cyclotron and Larmor frequency?
A: Larmor frequency is half the cyclotron frequency and describes precession rather than orbital motion.

Q5: Can this be used for ions in plasma?
A: Yes, this describes the gyration frequency of any charged particle in a magnetic field, fundamental to plasma physics.