How to study Cyclotron for class 12 physics part-4
It is a device developed by Lawrence and Livingstone and is used to accelerate charged particles like protons and deuterons. This results in the production of high energy beam which is then used for artificial disintegration, etc.
Suppose a deuteron is at the center of the gap and D1 is at negative potential compared to D2 then deuterons will be accelerated by the electric field between the dees towards D1. Since magnetic field B is perpendicular to the direction of motion of deuteron, a force will act on the particle given by
F = qv x B (where v and B are vectors) = qvB
Consequently, the particle moves along a circular path whose radius is given by
cyclotron 2 Cyclotron Working Principle
So time period and frequency are independent of the speed of charge and radius of the circular path. If this frequency is equal to the frequency of the oscillator then by the time particle complete half revolution the polarity of the field will change. Deuteron will again be accelerated across the gap, its velocity will increase so that now it will move in a circular path of greater radius but its frequency will not be affected and the process of acceleration continues.
The particle is thus accelerated to gain high velocity. Its kinetic energy increases and when the radius of the path reaches up to the value of the radius of the dee (R), a beam is deflected by a negatively charged plate. Therefore with r=R, its maximum kinetic energy will be
Cyclotron Working Principle
So the necessary condition for accelerating the deuterons is
cyclotron5 Cyclotron Working Principle
where f0 is oscillator frequency. This is called resonance condition.
As velocity attained is high, we choose heavier particles e.g., protons, deuterons for acceleration in the cyclotron. The reason is that at such high velocities, mass varies with velocity and f will then depend on velocity, upsetting the resonance condition. This variation in mass is more marked in the case of lighter particles. So cyclotron is suitable only for accelerating heavy particle like protons, deuterons a – particles etc.
Electrons cannot be accelerated by cyclotrons because the mass of an electron is very small and a small increase in energy of electron makes the electrons move with very high speed. As a result of it the electron goes quickly out of step with the oscillating electric field, it is for these reasons that other accelerating machines such as a synchrotron, betatron (for accelerating electrons) have been developed. Cyclotron cannot be used for accelerating uncharged particle like neutrons.
Cyclotron in India
Variable Energy Cyclotron Centre (VECC) is located in Calcutta, India. The Centre building itself houses a 224 cm cyclotron, was the first of its kind in India, has been operational since 1977-06-16. It provides proton, deuteron, an alpha particle and heavy ion beams of various energies to other institutions.
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- how cyclotron works
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- how to define Lorentz force
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