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An alternate electric field of frequency...

An alternate electric field of frequency v, is applied across the dees `(radius=R)` of a cyclotron that is being used to accelerate protons `("mass"=m)`. The operating magnetic field (b) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by

A

`(2pimf)/(e),2pi^(2)mf^(2)R^(2)`

B

`(2pi^(2)mf)/(e^(2)),4pi^(2)mf^(2)R^(2)`

C

`(pimf)/(e),pi^(2)mf^(2)R^(2)`

D

`(2pi^(2)m^(2)f^(2))/(e),2pi^(2)m^(2)f^(2)R^(2)`

Text Solution

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The correct Answer is:
A
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The cyclotron is a device which is used to accelerate charged particles such as protons, deutrons, alpha particles, etc. to very high energy. The principle on which a cyclotron works is based on the fact that an electric field can accelerate a charged particle and a magnetic field can throw it into a circular orbit. A particle of charge +q experiences a force qE in an electric field E and this force is independent of velocity of the particle. The particle is accelerated in the direction of the magnetic field. On the other hand, a magnetic field at right angles to the direction of motion of the particle throws the particle in a circular orbit in which the particle revolves with a frequency that does not depend on its speed. A modest potential difference is used as a sources of electric field. If a charged particle is made to pass through this potential difference a number of times, it will acquire an enormous by large velocity and hence kinetic energy. Which of the following cannot be accelerated in a cyclotron?

The cyclotron is a device which is used to accelerate charged particles such as protons, deutrons, alpha particles, etc. to very high energy. The principle on which a cyclotron works is based on the fact that an electric field can accelerate a charged particle and a magnetic field can throw it into a circular orbit. A particle of charge +q experiences a force qE in an electric field E and this force is independent of velocity of the particle. The particle is accelerated in the direction of the magnetic field. On the other hand, a magnetic field at right angles to the direction of motion of the particle throws the particle in a circular orbit in which the particle revolves with a frequency that does not depend on its speed. A modest potential difference is used as a sources of electric field. If a charged particle is made to pass through this potential difference a number of times, it will acquire an enormous by large velocity and hence kinetic energy. Cyclotron is not suitable for accelerating

The cyclotron is a device which is used to accelerate charged particles such as protons, deutrons, alpha particles, etc. to very high energy. The principle on which a cyclotron works is based on the fact that an electric field can accelerate a charged particle and a magnetic field can throw it into a circular orbit. A particle of charge +q experiences a force qE in an electric field E and this force is independent of velocity of the particle. The particle is accelerated in the direction of the magnetic field. On the other hand, a magnetic field at right angles to the direction of motion of the particle throws the particle in a circular orbit in which the particle revolves with a frequency that does not depend on its speed. A modest potential difference is used as a sources of electric field. If a charged particle is made to pass through this potential difference a number of times, it will acquire an enormous by large velocity and hence kinetic energy. The working of a cyclotron is based on the fact that

The Betatron was the first important machine for producing high energy electrons. The action of the betatron depends on the same fundamental principle as that of the transformer in which an alternating current applied to a primary coil induces an altermating current usually with higher or lower voltage in the secondary coil. In the betatron secondary coil is replaced by a doughnut shaped vacuum chamber.Electron produced in the doughnut from a hot filament, are given a preliminary acceleration by the application of an electric field having potential difference of 20 kV to 70 kV , when an alternating magnetic field is applied parallel to the axis of the tube, two effects are produced (1) an electromotive force is produced in the electron orbit by the changing magnetic flux that gives an additional energy to the electrons (2) a radial force is produced by the action of magnetic field whose direction is perpendicular to the electron velocity. Which keeps the electron moving in a circular path. Conditions are arranged such that the increasing magnetic field keeps the electron in a circular orbit of constant radius. The mathematical relation between the betatron parameters to ensure the above condition is called BETATRON condition. If the orbit radius of the circular path traced by the electron is R , magnetic field is B , speed of the electron is v , mass of the electron is m , charge on the electron is e and phi is the flux within the orbit of radius R . Then answer the following questions based on the above comprehension. What is the value of (d(m|vecv|))/(dt) ?

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