Question

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.

Answer 1

 Schematic sketch of cyclotron:

The combination of crossed electric and magnetic fields is used to increase the energy of the charged particle. Cyclotron uses the fact that the frequency of revolution of the charged particle in a magnetic field is independent of its energy. Inside the dees the particle is shielded from the electric field and magnetic field acts on the particle and makes it to go round in a circular path inside a dee. Every time the particle moves from one dee to the other it comes under the influence of electric field which ensures to increase the energy of the particle as the sign of the electric field changed alternately. The increased energy increases the radius of the circular path so the accelerated particle moves in a spiral path.

Since radius of trajectory,

`r =(vm)/(qB)`

`therefore v = (rqB)/m`

Hence, the kinetic energy of ions,

`1/2 mv^2`

`1/2 m (r^2 q^2 B^2)/m^2`

`= 1/2 (r^2q^2B^2)/m`