(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 ?

Explanation

### Solution

#### Part (a): Schematic Sketch and Explanation of Cyclotron

1. **Schematic Sketch**:
- Draw two semi-circular "D" shaped electrodes (called "dees") placed back to back with a gap in between.
- Indicate a magnetic field directed perpendicular to the plane of the dees.
- Show a particle (like a proton or alpha particle) starting from the center and moving in a circular path within the dees.
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