Explain the working of a cyclotron and give its uses.

(N/A) The figure shows a schematic view of the cyclotron.
Inside the metal boxes (dees),the particle is shielded and is not acted upon by the electric field. The electric field prevails only in the gap between the two dees.
The magnetic field acts on the particle and forces it to move in a circular path inside the dee.
Every time the particle moves from one dee to another,it is accelerated by the electric field.
The polarity of the electric field is reversed in synchronization with the circular motion of the particle.
This ensures that the particle is always accelerated by the electric field. Each acceleration increases the kinetic energy of the particle. As energy increases,the radius of the circular path increases,resulting in a spiral path.
Charged particles (e.g.,protons) move in a semicircular path in one of the dees and arrive in the gap between the dees in a time interval of $\frac{T}{2}$,where $T$ is the time period of revolution.
$T = \frac{1}{v_{c}} = \frac{2 \pi m}{q B}$ or $v_{c} = \frac{q B}{2 \pi m} \quad \dots (1)$
This frequency is called the cyclotron frequency and is denoted by $v_{c}$. It is independent of the speed,momentum,and kinetic energy of the particle.
The uses of a cyclotron are as follows:
$(1)$ The high-energy particles produced in a cyclotron are used to bombard nuclei to study nuclear reactions and investigate nuclear structure.
$(2)$ It is used to implant ions into solids to modify their properties or to synthesize new materials.
$(3)$ It is used to produce radioactive isotopes,which are utilized in hospitals for medical diagnosis and treatment.