Question

Draw a schematic diagram of a cyclotron. Explain its underlying principle and working, stating clearly the function of the electric and magnetic fields applied on a charged particle.
Deduce an expression for the period of revolution and show that it does not depend on the speed of the charged particle.

Answer 1

Cyclotron : It is a device by which positively charged particles like protons, deutrons, etc. can be accelerated.
Principle : A positively charged particle can be accelerated by making it to cross the same electric field repeatedly with the help of a magnetic field.
Construction : It consists of two semi-cylindrical boxes `D_(1) and D_(2)`, called dees enclosed in an evacuated chamber. The chamber is kept between the poles of a powerful magnet so that uniform magnetic field acts perpendicular to the plane of the dees. An alternating voltage is applied in the gap between the two dees by using a high frequency oscillator. The electric field is zero inside the dees.
Working and theory : At a certain instant, let `D_(1)` be positive and `D_(2)` be negative. The radius of the circular path is given by
`qv B=mv^()//r or r=mv//qB`
Period of revolution,
`T=(2pir)/(v)-(2pi)/(v). (mv)/(qB)=(2pi m)/(qB)`
Frequency of revolution `f=(1)/(T)=(qB)/(2pi m)`
Clearly, frequency f is independent of both v and r and is called cyclotron frequency. If the frequency of applied a.c. is equal to f, then every time the proton reaches the gap between the dees, the direction of electric field is reversed and proton receives a push and finally it gains very high kinetic energy. The proton follows a spiral path. The accelerated protons are deflected protons are deflected towards the target.