$A$ cyclotron's oscillator frequency is $20 MHz$. The operating magnetic field for accelerating protons is (charge of proton $= 1.6 \times 10^{-19} C$,mass of proton $= 1.67 \times 10^{-27} kg$). (in $T$)

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.

The cyclotron frequency of an electron gyrating in a magnetic field of $1\, T$ is approximately

In the cyclotron, as the radius of the circular path of the charged particle increases, ($\omega$ = angular velocity, $V$ = linear velocity)

$A$ cyclotron is used to accelerate

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 $q = 1.6 \times 10^{-19} \,C$)