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(m/(qB). (b) What is the frequency f? (c) What is the angular velocity (ω 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 22.6-4 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.
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(m/(qB). (b) What is the frequency f? (c) What is the angular velocity (ω 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 22.6-4 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.
(a) Show that the period of the circular orbit of a charged particle moving perpendicularly to a uniform magnetic field is T = 2(m/(qB). (b) What is the frequency f? (c) What is the angular velocity (ω 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 22.6-4 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.
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
Question 1
For an eleciric field of 2.5 x 10 V/m, what is the
sırength of the magnetic field needed to pass an elec-
tron of speed 2.2 x 105 m/s with no deflection? Draw
the muually perpendicular a, Ē, and Ē directions that
allow this to Occur.
A proton, that is accelerated from rest through a potential of 14.0 kV enters the velocity filter, consisting of a parallel-plate capacitor and a
magnetic field, shown below.
112
The E-field between the parallel capacitor plates is 1.1.105 N/C. What B-field is required so that the protons are not deflected? (Ignore relativistic
effects for high velocities.)
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1. A beam of electrons whose kinetic energy is Kemerges from a thin-foil "window" at the end of an
accelerator tube. Ametal plate at distance d from this window is perpendicular to the direction of the
emerging beam. What minimum strength uniform magnetic field could you apply to prevent the beam from
hitting the metal plate? Express your final answer in terms of K, d, and any known constants.
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