Which of the following is the correct expression for cyclotron frequency?

Correct option is D

Cyclotron: A cyclotron works on the principle that an electric field accelerates a charged particle, and the magnetic field keeps it revolving in circular orbits with a constant frequency.

This device is a type of particle accelerator in which a perpendicular magnetic field is applied to the particle's motion plane, causing it to move in a circular path.

$$\text{Magnetic Force and Centripetal Force:} \\\text{The relationship between the magnetic force and the centripetal force is given by the equation:} \\Bqv = \frac{mv^2}{r} \\\text{Simplifying this equation, we find the velocity of the particle } v \text{ as:} \\v = \frac{Bq}{m} \\\text{The angular velocity } \omega \text{ and radius } r \text{ also relate in such a way that:} \\\omega \times r = \frac{Bq}{m} \\\text{From this, we derive the expression for angular velocity } \omega: \\\omega = \frac{Bq}{m} \\\text{The cyclotron frequency } V_C \text{ is given by the formula:} \\V_C = \frac{qB}{2\pi m}$$​​