PHYSICS / CHARGED PARTICLE MOTION
Calculate the nonrelativistic orbital frequency of a charged particle in a uniform magnetic field.
METHOD / WORKED EXAMPLE
Cyclotron frequency depends on charge-to-mass ratio and magnetic field, but not orbit radius or speed in the ideal nonrelativistic model.
WORKED DEFAULT
For a proton charge of 1.60218e-19 C, mass 1.67262e-27 kg, and 1.5 T field, frequency is about 22.87 MHz and period is about 43.73 ns.
READ THE RESULT
Increasing field or charge raises frequency; increasing mass lowers it. At relativistic speeds, gamma changes the orbital response and this simple frequency is no longer sufficient.
ASSUMPTIONS AND LIMITS
Motion is nonrelativistic in a uniform field, velocity is perpendicular to the field, and electric fields or collisions are neglected.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
COMMON QUESTIONS
In the ideal nonrelativistic derivation, magnetic force qvB supplies centripetal force mv squared over r. Combining that radius with circumference divided by speed cancels v, leaving period dependent on mass, charge, and field. Relativistic mass-energy behavior breaks this simple independence at sufficiently high particle speeds.
Enter the charge magnitude. The sign of charge determines the direction of curvature, not the positive orbital frequency magnitude returned here. To model clockwise versus counterclockwise motion, keep the sign and field direction in a separate vector or right-hand-rule analysis with a stated coordinate system.
It is a first ideal check, not a complete equipment setting. Relativistic shifts, field nonuniformity, focusing, extraction geometry, harmonics, acceleration gaps, and particle losses can alter operation. Use the result only inside a controlled design validated against the specific accelerator, instrumentation, and documented operating procedure.
RELATED TOOLS
Use boundary
Invert the magnetic-orbit period after balancing magnetic and centripetal forces. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
f = |q|B / (2 pi m)