Cyclotron Frequency of Charged Particle

What is this formula?

This formula calculates the cyclotron frequency of a charged particle moving perpendicular to a uniform magnetic field. The frequency depends on the particle charge, mass, and magnetic field strength.

When to use it

Use this formula when analyzing circular motion of charged particles in magnetic fields, such as in cyclotrons, mass spectrometers, plasma physics, and geomagnetic particle motion.

Example

Calculate the cyclotron frequency of a proton moving in a magnetic field of 0.8 T.

Data:

q = 1.602 × 10^-19 C

m = 1.673 × 10^-27 kg

B = 0.8 T

Formula:

f = abs(q)*B/(2*pi*m)

Substitution:

f = (1.602*10^-19*0.8)/(2*pi*1.673*10^-27)

Result:

f = 1.22 × 10^7 Hz

Applications

- Cyclotron particle accelerators

- Mass spectrometry

- Plasma confinement

- Space physics

- Charged particle motion in Earth's magnetic field