Question

(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 a–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?

Answer 1

Role of electric field (i) Electric field accelerates the charge particle passing through the gap with the help of electric oscillator. 

(ii) Electric oscillator imparts the energy to charged particle till it comes out from the exit slit. 

Role of magnetic field 

As the accelerated charge particle enters normally to the uniform magnetic field, it exerts a magnetic force in the form of centripetal force and charge particle moves on a semicircular path of increasing radii in each dee (D₁ or D₂).

So, proton acquires higher velocity at the exit slit for fixed radius r ≤ R, where R is the radius of the dee.