Question

(i) Draw a neat and labelled diagram of a cyclotron
(ii) State the underlying principle and explain how a positively charged particle gets accelerated in the machine ?.
(iii) Show mathematically that the cyclotron frequency does not depend upon the speed of the particle

Answer 1

(i) The diagram of cyclotron is as follow in the image:

(ii)Principle of cyclotron is it is used to accelerate positive charged particle like  protons and deutrons in the presence of uniform magnetic field.

• A cyclotron has two hallow semicircular electrodes known as dees, separated by narrow gap in evacuated chamber.An electric field is created in gap by radio frequency oscillator.
• When a particle jump from one dee to another dee it gain energy so the kinetic energy and speed increases with increase of speed of particle.
• Radius of particle also increases and maximum radius of of circular path is equal to radius of dee and speed of particle is also maximum.
• Due to this accelerated particle electric field is developed perpendicular to the magnetic field.

(iii) Frequency of cyclotron is reverse of time period . The time of cyclotron is as given  T=2pim/qB  where, m is mass of particle B is the magnetic field and q is the charge of particle which is accelerated in cyclotron.

• Frequency of charged particle is f =1/T
• So f=qB/2pim  hence from the formula it is clear that frequency of cyclotron do not depend on velocity of particle.

The diagram of cyclotron is in diagram attached.