A charged particle (charge $q$, mass $m$) moves in a circle perpendicular to a uniform magnetic field $B$. The frequency of revolution (the CYCLOTRON FREQUENCY) is

1. The magnetic force provides the centripetal force: $qvB = \dfrac{mv^2}{r}$, so $r = \dfrac{mv}{qB}$. 2. Period of revolution: $T = \dfrac{2\pi r}{v} = \dfrac{2\pi m}{qB}$. 3. Frequency: $f = 1/T = \dfrac{qB}{2\pi m}$. This is the CYCLOTRON FREQUENCY. 4. KEY: the frequency is INDEPENDENT of the particle's speed (in the non-relativistic regime) — this is what makes the cyclotron work as an accelerator. 5. Option A is the ANGULAR frequency $\omega = qB/m$, not the cycles-per-second $f$. Option C inverts dimensions. Option D is the period, not the frequency. _Source: NCERT Class 12 Physics Part 1, Ch 4, §4.4.2 (Cyclotron motion), p. 9–10._