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प्रश्न
Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.
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उत्तर
The frequency va of the applied voltage (radio frequency) is adjusted so that the polarity of the dees is reversed at the same time that it takes the ions to complete one-half of the revolution. The requirement va = vc is called the resonance condition.
When the frequency of the radio frequency (rf) field was doubled, then the resonance condition are violated and the time period of the radio frequency (rf) field was halved. Therefore, the duration in which a particle completes half revolution inside the dees, radio frequency completes the cycle.
So, particles will accelerate and decelerate alternatively. So, the radius of path in the dees will remain the same.
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संबंधित प्रश्न
Draw a neat labelled diagram for the construction of 'cyclotron'
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 underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies
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.
Obtain the expression for the cyclotron frequency.
A proton and an electron travelling along parallel paths enter a region of uniform magnetic field, acting perpendicular to their paths. Which of them will move in a circular path with higher frequency?
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?
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.
Figure shows a rod PQ of length 20.0 cm and mass 200 g suspended through a fixed point O by two threads of lengths 20.0 cm each. A magnetic field of strength 0.500 T exists in the vicinity of the wire PQ, as shown in the figure. The wires connecting PQ with the battery are loose and exert no force on PQ. (a) Find the tension in the threads when the switch S is open. (b) A current of 2.0 A is established when the switch S is closed. Find the tension in the threads now.
Two metal strips, each of length l, are clamped parallel to each other on a horizontal floor with a separation b between them. A wire of mass m lies on them perpendicularly, as shown in the figure. A vertically-upward magnetic field of strength B exists in the space. The metal strips are smooth but the coefficient of friction between the wire and the floor is µ. A current i is established when the switch S is closed at the instant t = 0. Discuss the motion of the wire after the switch is closed. How far away from the strips will the wire reach?
(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?
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.
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 ______.
A particle of mass m is moving in a circular path of constant radius r such that, its centripetal acceleration ac is varying with time t as ac = k2rt2, where k is a constant. The power delivered to the particle by the forces acting on it is ______.
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
