A. Obtain the expression for the cyclotron frequency.

B. A deuteron and a proton are accelerated by the cyclotron. Can both be accelerated with the same oscillator frequency? Give reason to justify your answer.

A. The cyclotron is used to accelerate charged particles to very high energies. The cyclotron exploits both electric and magnetic fields in combination to increase the energy of particles. The frequency of revolution of a charged particle in a magnetic field is independent of its energy. Inside the Dees of the cyclotron the particle is not affected by the electric field. The magnetic field acts on the particle and makes it go around in a circular path inside a dee. Every time the particle passes from one dee to another it is gets accelerated by the electric field. The sign of the electric field is changed alternately in tune with the circular motion of the particle. Each time the acceleration increases the energy of the particle. The particles move in a semi-circular path in one of the Dees and arrive in the gap between the Dees in a time interval T/2; where T, the period of revolution, is given by,

This frequency is called the cyclotron frequency.

B. A deuteron and proton might have same charge but they cannot be accelerated through the same cyclotron/oscillator frequency as deuteron has more mass than proton and thus will have less frequency.