Cyclotron Frequency

f = \frac{qB}{2\pi m}

Frequency of circular motion of charged particle in magnetic field.

Variables

Frequency

Cyclotron frequency

In SI units: s⁻¹

Allowed values: greater than 0

Charge

Particle charge

In SI units: A·s

Magnetic field

Field strength

In SI units: kg/(A·s²)

Mass

Particle mass

Allowed values: 0 or more

Derivation

From qvB = mv²/r and ω = v/r, f = ω/(2π) = qB/(2πm).

Your notes

0/5000

Check value

Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

q = 2 C (Charge)
B = 3 T (Magnetic field)
m = 4 kg (Mass)

Result: f = 0.23873241 Hz

Other electricity & magnetism formulas with the same quantities

Hall Voltage (Magnetism) shares Magnetic field, Charge
Magnetic Force on Wire (Magnetism) shares Magnetic field
Magnetic Field (Long Wire) (Magnetism) shares Magnetic field
Magnetic Field (Solenoid) (Magnetism) shares Magnetic field
Energy Density (Magnetic Field) (Magnetism) shares Magnetic field
Electric Potential Energy (Electrostatics) shares Charge

Where this formula is listed

Electricity & Magnetism formulas, under Magnetism, alongside Biot-Savart Law and Ampere's Law.
In the electricity & magnetism list it comes after Energy Density (Magnetic Field) and before Cyclotron Radius.
Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Cyclotron Frequency formula?

Cyclotron Frequency is written f = qB/(2πm). Frequency of circular motion of charged particle in magnetic field. It belongs to Electricity & Magnetism, under Magnetism.

What are the units in f = qB/(2πm)?

In SI units, f is frequency, measured in s⁻¹; q is charge, measured in A·s; B is magnetic field, measured in kg/(A·s²); m is mass, measured in kg.

How is the Cyclotron Frequency formula derived?

From qvB = mv²/r and ω = v/r, f = ω/(2π) = qB/(2πm). The result is f = qB/(2πm).