Cyclotron

A cyclotron is a particle accelerator that is used to accelerate charged particles, typically protons or ions. A cyclotron consists of two hollow, D-shaped metal electrodes, called "dees," that are placed facing each other in a strong magnetic field. The dees are connected to an alternating current (AC) power supply, which creates an oscillating electric field between them. Charged particles are injected into the space between the dees and are accelerated by the oscillating electric field.

As the particles are accelerated, they move in a circular path around the magnetic field lines, due to the Lorentz force. The radius of the circular path is determined by the strength of the magnetic field and the energy of the particles.

As the particles complete each circular orbit, they pass through a gap in one of the dees and enter the space between the dees again, where they are accelerated by the electric field. The process is repeated many times, with the particles gaining energy on each pass through the dees, until they reach the desired energy.

A charged partcle moving with velocity $\vec{v}$ in electric field $\vec{E}$ and magnetic field $\vec{B}$ experience Lorentz force \begin{align} \vec{F}=q\vec{E}=q\vec{v}\times\vec{B}. \end{align}

The magnetic force $qvB$ provides the centripetal acceleration i.e., \begin{align} qvB=m\frac{v^2}{r} \end{align} The time period is \begin{align} T=\frac{2\pi r}{v}=\frac{2\pi m}{qB}. \end{align} The cyclotron frequency is \begin{align} \omega=\frac{2\pi}{T}=\frac{qB}{m}. \end{align}

Problems from IIT JEE

Problem (JEE Mains 2022): A cyclotron is used to accelerate protons. If the operating magnetic field is 1.0 T and the radius of cyclotron "dees" is 60 cm, the kinetic energy of the accelerated protons will be

1. 12 MeV
2. 18 MeV
3. 16 MeV
4. 32 MeV

Problems (JEE Mains 2022): A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle

1. 1:1
2. 1:2
3. 2:1
4. 1:4

Problem (JEE Mains 2021): The maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is______

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