Advertisements
Advertisements
प्रश्न
Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.
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.
APPEARS IN
संबंधित प्रश्न
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.
Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic field in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles.
Which of the following particles will describe the smallest circle when projected with the same velocity perpendicular to a magnetic field?
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.
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?
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?
The life time of muon in the rest frame is 2 × 10-6 sec. A beam of muons emerges from a cyclotron with velocity where c is the velocity of light The mean life of muons observed in the laboratory frame will be ______.
In a cyclotron, a charged particle ______.
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
