Write working principle of cyclotron and with a suitable diagram explain its working. Give any two applications of cyclotron.
Answers
Answer:
Principle
Cyclotron works on the principle that a charged particle moving normal to a magnetic field experiences magnetic lorentz force due to which the particle moves in a circular path.
Construction
It consists of a hollow metal cylinder divided into two sections D1 and D2 called Dees, enclosed in an evacuated chamber (Fig 3.21). The Dees are kept separated and a source of ions is placed at the centre in the gap between the Dees. They are placed between the pole pieces of a strong electromagnet. The magnetic field acts perpendicular to the plane of the Dees. The Dees are connected to a high frequency oscillator.
Working:
When a positive ion of charge q and mass m is emitted from the source, it is accelerated towards the Dee having a negative potential at that instant of time. Due to the normal magnetic field, the ion experiences magnetic lorentz force and moves in a circular path. By the time the ion arrives at the gap between the Dees, the polarity of the Dees gets reversed. Hence the particle is once again accelerated and moves into the other Dee with a greater velocity along a circle of greater radius. Thus the particle moves in a spiral path of increasing radius and when it comes near the edge, it is taken out with the help of a deflector plate (D.P). The particle with high energy is now allowed to hit the target T.
When the particle moves along a circle of radius r with a velocity v, the magnetic Lorentz force provides the necessary centripetal force.
Bqv = (vm2 ) / r
v /r = Bq / m = constant ...(1)
The time taken to describe a semi-circle
t = π r / v (2)
Substituting equation (1) in (2),
t = π m/ Bq .. (3)
It is clear from equation (3) that the time taken by the ion to describe a semi-circle is independent of
(i) the radius (r) of the path and (ii) the velocity (v) of the particle
Hence, period of rotation T = 2t
T = 2 π m / Bq = constant ...(4)
So, in a uniform magnetic field, the ion traverses all the circles in exactly the same time. The frequency of rotation of the particle,
v = 1 /T = Bq / 2 πm .. (5)
If the high frequency oscillator is adjusted to produce oscillations of frequency as given in equation (5), resonance occurs.
Explanation:
Working principle, working and applications of cyclotron are:--
Principle :-- A cyclotron accelerates charged particle using high frequency alternating voltage applied between two hollow shaped D metal electrodes inside vacuum chamber.
The dees are faced opposite to each other and are located between large electromagnet which applies magnetic field which causes particle to bend in circle due to Lorentz force perpendicular to direction of motion.
Working:--When particle jump from one dee to another it gain energy so kinetic energy and speed increases with increase of speed of particle radius of particle also increases.
Maximum radius of circular path is equal to radius of dee and under this condition speed of particle is maximum. Frequency of cyclotron is called as cyclotron frequency given by:-
f=qB/2piem
Where B is magnetic field, q is electric charge of particle and m is mass of charged particle.
So particle move in spiral motion.
Radius is given by r=mv/qB where v is velocity of charged particle.
Applications of cyclotron are:--
1)Used in particle therapy to treat cancer.
2)Used for research purposes, for chemical and particle analysis.
