Cyclotron Frequency And Energy Gain — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Cyclotron Frequency and Energy Gain Applies to charged particles undergoing circular motion in a uniform magnetic field (cyclotron motion) and accelerating through a potential difference (particle accelerators). For circular motion, the magnetic force provides the centripetal force: qvB = mv 2 r . Solving for the angular frequency : = qB m . The cyclotron frequency f is / 2 : f = qB 2 m . For energy gain, the work done by the electric field ( W ) equals the change in kinetic energy ( K ): W = qV gap = K . Mass (m) must be non-zero. The magnetic field (B) must be uniform. The particle must be charged (q 0). Confusing the magnetic force ( qvB ) with the centripetal force ( mv 2/r ) direction or magnitude. Forgetting the 2 factor when converting angular frequency ( ) to linear frequency ( f ). Assuming the energy gain is proportional to the particle's current kinetic energy rather than the gap voltage.