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प्रश्न
Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.
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उत्तर
Cyclotron is a machine used to accelerate charged particles or ions to high energies. It uses both electrical and magnetic fields in combination to increase the speed of the charged particles.
The particles move in two semi-circular containers D1 and D2, called Dees. Inside the metal box, the charged particle is shielded from external electric fields.
When the particle moves from one dee to another, electric field is acted on the particle.
The sign of the electric field is changed alternately, in tune with the circular motion of the particle. Hence, the particle is always accelerated by the electric field. As the energy of the particle increases, the radius of the circular path increases.
`qcB = (mv_2)/r`
`r= (mv)/(qB)`
Time taken for a particle for one complete revolution = T
`T = (2pir)/v`
T =`(2pim)/(qB)`
`T = 1/v_c`
Where `v_c`is the cyclotron frequency
Then,
`I/v_c = (2pim)/(qB)`
`v_c = (qB)/(2pim)`
The above expression is the expression for cyclotron frequency.
The oscillator applies an ac voltage across the Ds and this voltage must have a frequency equal to that of cyclotron frequency.
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संबंधित प्रश्न
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 underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies
An α-particle and a proton are released from the centre of the cyclotron and made to accelerate.
(i) Can both be accelerated at the same cyclotron frequency?
Give reason to justify your answer.
(ii) When they are accelerated in turn, which of the two will have higher velocity at the exit slit of the does?
(a) An electron moves along a circle of radius 1 m in a perpendicular magnetic field of strength 0.50 T. What would be its speed? Is it reasonable? (b) If a proton moves along a circle of the same radius in the same magnetic field, what would be its speed?
Assertion: The frequency of circular motion of a charged particle in cyclotron is independent of the mass of the particle.
Reason: Greater the mass of the particle less will be the frequency of the particle.
Which of the following is not correct about cyclotron?
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Its centripetal acceleration is ______.
The cyclotron was designed by ______
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
