In the year 1929-30, scientist Lawrence invented a particle accelerator device called the cyclotron. A cyclotron contains a hollow cylinder divided into two Dees in a vacuum chamber in which the charged particles are accelerated under the influence of an electric field along a spiral path.

Principle of cyclotron:-

The working principle of a cyclotron is that the charged particle is accelerated by the electric field and the force on the charged particle will be given by Lorentz force.

F=Bqv

Here q is the charge on the particle.E is the electric field under which the charged particle is accelerated. B is the static magnetic field on the particle.v is the velocity of the charged particle.

Working of the cyclotron:

Cyclotron consists of a  hollow cylinder divided into two parts called Dees. These Dees are   placed in a vacuum chamber. Now this Dees are connected with the high frequency oscillators.

When the positive charge having a mass m is released from the source then the negative charged dee attracts the particle now the Lorentz force acts on the particle which moves the particle in a spiral path.

When the charged particle reaches the gap between the dees, then the polarity of the dees are changed so the dee just in front of the moving charged particle now becomes negative and attracts the particle and accelerates the particle. Now the charged particle again comes to the gap between the dees, then again the polarity is changed.

Thus in this way by continuing changing the polarity of the dees and under the influence of the Lorentz force the charged particle is accelerated in the cyclotron.

Velocity, period and frequency of a charged particle:

The lorentz force acting on a charged particle moving in a circular path will be equal to the centripetal force acting on the particle.

Bqv=1 ⁄ 2mv²

v= √2Bqv ⁄ m

Thus the velocity of the charged particle will be calculated by the above formula.

Now again from the above equation

Bqv=1 ⁄ 2mv²

v ⁄ r=Bq ⁄ m

Now time for half circle is given as:

t=πr ⁄ v 

t= πm ⁄ Bq

Total time period of the accelerated particle 

T=2πm ⁄ Bq

So the frequency of the charged particle will be given as

f=Bq ⁄ 2πm

Application of Cyclotron:

1. The accelerated charged particles by the cyclotron are used to bombard the atomic nuclei in the nuclear physics experiments.
2. Cyclotrons are also used in the treatment of cancer in radiation therapy.
3. The charged particles of the cyclotrons are used in changing nuclear structure or in nuclear transmutation.

Limitation of cyclotron:

1. Cyclotrons can not be used to accelerate the neutrons because they are neutral so there will not be any effect of magnetic or electric field on this particle.
2. Electrons can not be accelerated by the cyclotrons because the electrons have very small mass; their speed increases rapidly by which the resonance between the voltage and the particle is lost.
3. It is very difficult to maintain a uniform electric field over a large area of the dees.

 Conclusion:

In this article we have studied the working of the cyclotron. A cyclotron is a particle accelerator device that increases the speed of the protons under the influence of the normal magnetic field and the Lorentz force. Cyclotrons are used in many areas in the medical field for the treatment of cancer in the nuclear research field.