If $q$ is the electric charge,$B$ is the magnetic field,$R$ is the dee radius,and $m$ is the mass of ions,the kinetic energy of the ions in a cyclotron is given by

Discuss the motion of a charged particle in a uniform magnetic field with initial velocity perpendicular to the magnetic field. $OR$ Explain the principle of a cyclotron.

$A$ cyclotron's oscillator frequency is $10 \text{ MHz}$ and the operating magnetic field is $0.66 \text{ T}$. If the radius of its dees is $60 \text{ cm}$, then the kinetic energy of the proton beam produced by the accelerator is: (in $\text{ MeV}$)

$A$ cyclotron's oscillator frequency is $n$ and the radius of the dees is $r$. The operating magnetic field $(B)$ for accelerating protons of charge $q$ and the kinetic energy of the protons produced by the accelerator are respectively ($m$ and $v$ are the mass and velocity of the proton).

$A$ cyclotron is used to accelerate protons $\left({ }_{1}^{1} H\right)$,deuterons $\left({ }_{1}^{2} H\right)$,and $\alpha$-particles $\left({ }_{2}^{4} He\right)$. While exiting under similar conditions,the minimum kinetic energy $(KE)$ is gained by:

In a cyclotron experiment, if we assume that the maximum radius attained by any charged particle is equal to the radius of the dees, then the minimum kinetic energy gained by the particles will be for