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Integrated Concepts (a) Show that the period of the
Chapter 22, Problem 80(choose chapter or problem)
Integrated Concepts
(a) Show that the period of the circular orbit of a charged particle moving perpendicularly to a uniform magnetic field is \(T=2 \pi m /(q B)\)
(b) What is the frequency \(f\) ?
(c) What is the angular velocity \(\omega\) ? Note that these results are independent of the velocity and radius of the orbit and, hence, of the energy of the particle. (Figure \(22.64\).)
Figure \(22.64\) Cyclotrons accelerate charged particles orbiting in a magnetic field by placing an AC voltage on the metal Dees, between which the particles move, so that energy is added twice each orbit. The frequency is constant, since it is independent of the particle energy—the radius of the orbit simply increases with energy until the particles approach the edge and are extracted for various experiments and applications.
Equation Transcription:
Text Transcription:
T=2 pi m/(qB)
f
omega
22.64
Questions & Answers
QUESTION:
Integrated Concepts
(a) Show that the period of the circular orbit of a charged particle moving perpendicularly to a uniform magnetic field is \(T=2 \pi m /(q B)\)
(b) What is the frequency \(f\) ?
(c) What is the angular velocity \(\omega\) ? Note that these results are independent of the velocity and radius of the orbit and, hence, of the energy of the particle. (Figure \(22.64\).)
Figure \(22.64\) Cyclotrons accelerate charged particles orbiting in a magnetic field by placing an AC voltage on the metal Dees, between which the particles move, so that energy is added twice each orbit. The frequency is constant, since it is independent of the particle energy—the radius of the orbit simply increases with energy until the particles approach the edge and are extracted for various experiments and applications.
Equation Transcription:
Text Transcription:
T=2 pi m/(qB)
f
omega
22.64
ANSWER:
Solution 80PE
(a)
The radius of curvature of the path of a charged particle is,
r=
Here r is radius curvature of the path of a charged particle, m is mass of charged particle,