Home
Class 12
PHYSICS
Answer the following: (i) Obtain the e...

Answer the following:
(i) Obtain the expression for the cyclotron frequency.
(ii) A deuteron and a proton are accelerated by the cyclotron. Can both be accelerated with the same oscillator frequency ? Give reason to justify your answer.

Text Solution

Verified by Experts

(i) In a cyclotron, centripetal force is provided by the magnetic field to a charged particle which helps the particle in moving in a circular path. Equating the two forces we have
`(mv^(2))/(r )= qvB`
`rArr v - (qBr)/(m)`
Period of Revolution `T = (2pir)/(v) = (2pir)/(qBr) .m`
`rArr T = (2pim)/(qB)`
The frequency of particle in a cyclotron,
`v - 1/T = (qB)/(2pim)` Ang. frequency `= omega = (2pi)/(T) = (Bq)/(m)`.
(ii) A cyclotron works only when the frequency of the revolution of particle is equal to the frequency of oscillation.
`:.` Mass of proton and deutron are different `(m_(3) = 2m_(P))` and `v alpha = 1/(m)`.
`:.` The frequency of revolution of proton and deutron is different.Hence, they can't be accelerated with the same oscillator frequency.
Promotional Banner

Topper's Solved these Questions

  • XII BOARDS

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise SET-I (SECTION-D)|1 Videos

  • XII BOARDS

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise SET-I (SECTION-E)|5 Videos

  • XII BOARDS

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise SET-I (SECTION-B)|5 Videos

  • SAMPLE PAPER 2019

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise SECTION D|6 Videos

Similar Questions

Explore conceptually related problems

(a) 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. (b) An alpha -particle and a proton are relased form 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 dees ?

Is it correct to say that any two right angles are congruent? Give reasons to justify your answer.

Can Q and S, both be metals ? Justify your answer.

Can two numbers have 12 as their H.C.F. and 234 as their L.C.M? Give reason to justify your answer.

Can a gas mixed with another gas forms a colloidal solution? Give reason for your answer.

Can all the angles of a quadrilateral be acute angles ? Give reason for your answer.

Can a triangle have two obtuse angles ? Give reason for your answer.

Can two numbers have 15 as their H.C.F. and 110 as their L.C.M.? Give reason to justify your answer.

Consider the following circuit : What would be the readings of the ammeter and the voltmeter when key is closed ? Give reason to justify your answers .

Which of the following particle can be accelerated in cyclotron?