$A$ particle of mass $m$ and charge $q$ is moving in a cyclotron with magnetic field $B$. The frequency of the circular motion of the particle is proportional to

If the maximum value of accelerating potential provided by a radio frequency oscillator is $12 \, kV$,the number of revolutions made by a proton in a cyclotron to achieve one-sixth of the speed of light is ....... .
$[m_p = 1.67 \times 10^{-27} \, kg, e = 1.6 \times 10^{-19} \, C, c = 3 \times 10^8 \, m/s]$

An alternating electric field of frequency $f$ is applied across the radius $R$ of a cyclotron to accelerate protons (mass $m$). The operating magnetic field $B$ used and kinetic energy $(K.E.)$ of the proton beam produced by it are respectively ($e=$ charge on proton).

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

The oscillator frequency of a cyclotron is $10 \,MHz$. What should be the operating magnetic field for accelerating protons (in $,T$)? (Given: mass of proton $m = 1.67 \times 10^{-27} \,kg$,charge of proton $q = 1.6 \times 10^{-19} \,C$)

Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency $(rf)$ field were doubled.