(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 –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 dees?
a)
The schematic sketch of cyclotron is as shown below:
Electric field: It helps in accelerating the charged particle passing through the gap with the help of electric oscillator. Electric oscillator imparts the energy to charged particle till it comes out from the exit slit.
Magnetic field: The magnetic force exerts a centripetal force when the accelerated charge particle enters normally to the uniform magnetic field. Centripetal force makes the particle move in a semicircular path of increasing radii in each Dee.
Kinetic energy acquired by the particle is given by,
b)
i) Now, using equation (1), we have
Here we can see that, cyclotron frequency depends upon (q/m) ratio.
So, 
That is, 
ii) Kinetic energy is given by, 
That is, 
That is, proton acquires higher velocity.
