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

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).

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

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.

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 ....... .
$[m_p = 1.67 \times 10^{-27} \, kg, e = 1.6 \times 10^{-19} \, C, c = 3 \times 10^8 \, m/s]$

In a cyclotron,the angular frequency of a charged particle is independent of