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Question
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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Solution
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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