Solved Examples on Cyclotron
Example 1: In a cyclotron the frequency of alternating current is 12 MHz. What should be the operating magnetic field to accelerate protons? Given mass of proton = 1.67 × 10-27 kg.
Solution:
Using formula for Cyclotron Frequency:
f = qB/2πm
Upon rearranging,
B = 2πmf/q
B = 2π × 1.67 × 10-27× 12 × 106/1.6 × 10-19
B = 0.79 T
Example 2: For the above problem, what is the kinetic energy of the proton beam produced by the cyclotron if the radius of the dee is 0.53 m?
Solution:
Using formula for Kinetic Energy:
E = q2B2r2/2m
E = (1.6 × 10-19)2(0.79)2(0.53)2/2 × 1.67 × 10-27
E = 1.34 × 10-12 J
In eV units,
E = 1.34 × 10-12 /1.6 × 10-19
E = 8.38 MeV
Example 3: The magnetic field inside a cyclotron is 0.8 T. At what maximum radius should a proton beam be extracted so that its energy is 10 MeV?
Solution:
Using formula for Kinetic Energy:
E = q2B2r2/2m
Upon rearranging,
r = √2mE/qB
r = √(2 × 1.67 × 10-27 × 107 × 1.6 × 10-19 )/1.6 × 10-19 × 0.8
r = 7.31 × 10-19/1.28 × 10-19
r = 5.71 m
Cyclotron
Cyclotron is a type of particle accelerator used to accelerate charged particles to high speeds. It was invented in 1929 by Ernest O. Lawrence. Cyclotrons are widely used in scientific research, medicine, and industry.
The basic principle of a cyclotron involves using a combination of electric and magnetic fields to accelerate charged particles along a circular path. This article covers the basics of cyclotron, including its definition, working, types, and other details related to it.
Table of Content
- What is a Cyclotron?
- Components and Operation of a Cyclotron
- Working Principle of Cyclotron
- Types of Cyclotrons
- Advantages of Cyclotron
- Limitations Of Cyclotron