Cyclotron Frequency Calculator
Find the cyclotron frequency of a charged particle in a magnetic field.
A charged particle circles in a magnetic field at the cyclotron frequency.
How the Math Works
The cyclotron frequency formula f = q·B ÷ (2π·m) calculates how fast a charged particle orbits in a magnetic field. Here, q represents the particle's charge, B is the magnetic field strength, and m is the particle's mass. The denominator 2π converts angular frequency to regular frequency, while the ratio q·B÷m determines the orbital rate based on the force balance between the magnetic field and the particle's motion.
Practical Applications
To use this calculation, determine the charge and mass of your particle (such as electrons, protons, or ions), measure the magnetic field strength in teslas, then apply the formula. For example, an electron with charge 1.6³⁻⁹ coulombs and mass 9.11–19⁃⁃⁃ kg in a 0.5 tesla field yields a cyclotron frequency of approximately 14 million cycles per second. This calculation is essential for designing particle accelerators, mass spectrometers, and understanding plasma confinement in fusion reactors.
Day-to-Day Use
While you may not calculate cyclotron frequencies daily, this principle enables technologies that impact everyday life. Medical MRI machines rely on nuclear magnetic resonance, which uses similar frequency principles to create detailed body images. Particle accelerators in medical treatments help cancer patients, and understanding charged particle behavior in magnetic fields improves our grasp of natural phenomena like the aurora borealis. Additionally, fusion research using these calculations brings us closer to clean, abundant energy for future generations.
Worked example
Electron in 1 T → about 28 GHz.
FAQ
Where is this used?
Cyclotrons, mass spectrometers and plasma physics.