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प्रश्न
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?
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उत्तर
Let a particle of charge q and mass m enter a region of magnetic field B with a velocity v normal to the field. The particle follows a circular path inside the cyclotron, and the necessary centripetal force is provided by the magnetic field.
Therefore, we have
`qvB=(mv^2)/r`
`:.r=(mv^2)/(qvB)=(mv)/(qB)`
Now, the time period of revolution will be
`T=d/v=(2pir)/v=(2pimv)/(qBv)=(2pim)/(qB)`
Therefore, from the above expression, we see that the time period is independent of the speed of the particle.
The time period should be independent of speed so that the frequency of revolution of the particle remains equal to the frequency of the ac source applied to the cyclotron.
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संबंधित प्रश्न
Which one of the following particles cannot be accelerated by a cyclotron?
(A) Electrons
(B) Protons
(C) Deuterons
(D) α- particles
In a cyclotron, magnetic field of 3·5Wb/m2 is used to accelerate protons. What should be the time interval in which the electric field between the Dees be reversed?
(Mass of proton = 1· 67 x 10-27Kg, Charge on proton =1·6x10-19c).
State the principle of a cyclotron.
Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.
Verify that the units weber and volt second are the same.
An electron is projected horizontally with a kinetic energy of 10 keV. A magnetic field of strength 1.0 × 10−7 T exists in the vertically upward direction.
(a) Will the electron deflect towards the right or left of its motion?
(b) Calculate the sideways deflection of the electron while travelling through 1 m. Make appropriate approximations.
A conducting wire of length l, lying normal to a magnetic field B, moves with a velocity v,as shown in the figure. (a) Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons concentrate at one end, resulting in an electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when the redistribution stops. (c) What potential difference is developed between the ends of the wire?
Answer the following question.
State the underlying principle of a cyclotron. Explain its working with the help of a schematic diagram. Obtain the expression for cyclotron frequency.
A cyclotron's oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its 'dees' is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator.
A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the ratio frequency field is doubled?
