How this calculator works
A magnetic force perpendicular to velocity bends a charged particle into a circular orbit without doing work. Equating that force to centripetal force gives an angular rate independent of speed in the nonrelativistic limit. Charge sign sets the sense of rotation, while its magnitude sets the frequency. Proton mass and charge defaults follow CODATA 2022. Parallel motion adds a helical pitch without changing this perpendicular orbit.
Formula
f = |q|B/(2 pi m), r = m v_perp/(|q|B), and v_perp = 2 pi f r.
Worked example
For |q| = 2 C, B = 3 T and m = 4 kg, f = 0.2387324 Hz. With the same values and perpendicular speed 6 m/s, the radius is 4 m.
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Frequently asked questions
Why does charge sign not change frequency?
It changes the direction of rotation. The number of cycles per second is a nonnegative magnitude.
Does this apply to relativistic particles?
No. Relativistic momentum introduces a Lorentz factor and lowers the frequency at a fixed field.
Which velocity belongs in the radius formula?
Use only the component perpendicular to the magnetic field; the parallel component does not bend.