Cyclotron

Consider a closed system of three charged particles with charges $3\mathrm{e},\mathrm{e}$ and $7\mathrm{e}$ respectively, where $\mathrm{e}$ is the electronic charge. Their corresponding masses are $6\mathrm{m},2\mathrm{m}$ and $14\mathrm{m}$ where $\mathrm{m}$ is the mass of electron. The particles may be moving in an arbitrary way. Then,

How do you calculate the number of revolutions in a cyclotron ?

State the principle of a cyclotron. Show that the time period of revolution of particles in a cyclotron is independent of their speeds. Why is this property necessary for the operation of a cyclotron?

A charged particle is moving in a uniform magnetic field in a circular path. The energy of the particle is doubled. If the initial radius of the circular path was R, the radius of the new circular path after the energy is doubled will be :

A charged particle of charge Q and mass m moves with velocity v in a circular path due to transverse magnetic field B, then its frequency is;
 
 
 
 

A cyclotron's oscillator frequency is $10\mathrm{MHz}$. What should be the operating magnetic field for accelerating protons? (mass of the proton $=1.67\times {10}^{-27} \mathrm{kg}$ )

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

A cyclotron is used to accelerate protons to a kinetic energy of $5 \mathrm{MeV}$. If the strength of magnetic field in the cyclotron is $2T$, Magnitude of radius and the frequency needed for the applied alternating voltage of the cyclotron is
(Given: Velocity of proton $=3\times {10}^7 \mathrm{m}/\mathrm{s}$).

A cyclotron is operating at a frequency of $12 \mathrm{MHz}$. Mass and charge of deuteron are $3.3\times {10}^{-27} \mathrm{kg}$ and $1.6\times {10}^{-19} \mathrm{C}$. To accelerate deutron, the necessary magnetic field is

A cyclotron is operating at a frequency of $12 \mathrm{MHz}$. Mass and charge of deuteron are $3.3\times {10}^{-27} \mathrm{kg}$ and $1.6\times {10}^{-19} \mathrm{C}$. To accelerate deuteron, the necessary magnetic field is

A proton of energy $100 \mathrm{eV}$ is moving in circular path in perpendicular magnetic field of ${10}^{-4} \mathrm{T}$. The cyclotron frequency of the proton in $\raisebox{1ex}{$\mathrm{radian}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$  will be

A cyclotron is accelerating deuterons having mass $2\times 1.6\times {10}^{-27} \mathrm{kg}$, charge $+e$ and $B=2 \mathrm{T}$. The maximum radius of the Dees required, if deuteron is to acquire $100 \mathrm{MeV}$ of energy, is

Cotyledons are also called-

A proton is accelerating on a cyclotron having oscillating frequency of $11 \mathrm{MHz}$in external magnetic field of $1 \mathrm{T}$. If the radius of its dees is $55 \mathrm{cm}$, then its kinetic energy (in $\mathrm{MeV}$) is ( $m_{\mathrm{p}}=1.67\times {10}^{-27}\mathrm{ }\mathrm{k}\mathrm{g},\mathrm{ }e=1.6\times \mathrm{ }{10}^{-19}\mathrm{ }\mathrm{C}$ )

An electron is moving in a cyclotron at a speed of $3.2\times {10}^7\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ in a magnetic field  $5\times {10}^{-4} \mathrm{T}$ perpendicular to it. The frequency of this electron is:$\left(q=1.6\times {10}^{-19}\mathrm{ }\mathrm{C},\mathrm{ }{m}_{\mathit{e}}=9.1\times {10}^{-31}\mathrm{ }\mathrm{k}\mathrm{g}\right)$

The operating magnetic field for accelerating protons in a cyclotron oscillator having frequency of $12\mathrm{ }\mathrm{M}\mathrm{H}\mathrm{z}$ is:$\left(\mathrm{q}=1.6\times {10}^{-19}\mathrm{ }\mathrm{C},\mathrm{ }{\mathrm{m}}_{\mathrm{p}}=1.67\times {10}^{-27}\mathrm{k}\mathrm{g}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }1\mathrm{ }\mathrm{M}\mathrm{e}\mathrm{V}=1.6\times {10}^{-13}\mathrm{J}\mathrm{ }\right)$

Which of the following is not correct about cyclotron?

The energy of emergent protons in $\mathrm{M}\mathrm{e}\mathrm{V}$ from a cyclotron having radius of its dees $1.8\mathrm{ }\mathrm{m}\mathrm{ }$ and applied magnetic field $0.7\mathrm{ }\mathrm{T}$ is: (mass of proton = $1.67\times {10}^{-27}\mathrm{ }\mathrm{k}\mathrm{g}$ )

A charged particle is moving in a cyclotron. What is the effect on the radius of path of this charged particle when the radio frequency field of cyclotron is doubled?

The cyclotron frequency ${\nu }_{\mathrm{c}}$ is given by: