Cyclotron Frequency Calculator

The movement of a charged particle in a uniform magnetic field is governed by the Lorentz force, which acts as a centripetal force pulling the particle into a circular path. By setting the magnetic force equation equal to the centripetal force equation, we can derive the fundamental formula for cyclotron frequency: f = (q * B) / (2 * π * m). In this equation, f represents the cyclotron frequency in hertz, q is the electrical charge of the particle in coulombs, B is the magnetic field strength in teslas, and m is the mass of the particle in kilograms. Additionally, the orbital velocity of the particle can be determined using the relationship v = 2 * π * f * r, where r is the radius of the circular path.

Let us calculate the cyclotron frequency for a single proton moving within a uniform magnetic field. Suppose we have a proton with a mass of approximately 1.673 × 10^-27 kg and an elementary charge of 1.602 × 10^-19 C, placed inside a magnetic field strength of 1.5 T. First, multiply the charge by the magnetic field: 1.602 × 10^-19 × 1.5 = 2.403 × 10^-19. Next, multiply two times pi by the mass of the proton: 2 × 3.14159 × 1.673 × 10^-27 = 1.051 × 10^-26. Finally, divide the numerator by the denominator: (2.403 × 10^-19) / (1.051 × 10^-26), which yields a cyclotron frequency of approximately 22.86 MHz.

Always ensure your input units are in standard SI units—coulombs for charge, kilograms for mass, teslas for magnetic field, and meters for radius—to avoid orders-of-magnitude errors. Remember that cyclotron frequency is independent of the particle's velocity or the radius of its orbit for non-relativistic speeds, meaning faster particles simply travel in larger circles while maintaining the exact same rotational period.