69. The cyclotron (Fig. 27-55 ) is a device used to accelerate elementary particles such as protons to high speeds. Part

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69 The Cyclotron Fig 27 55 Is A Device Used To Accelerate Elementary Particles Such As Protons To High Speeds Part 1 (49.91 KiB) Viewed 54 times

69. The cyclotron (Fig. 27-55 ) is a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some Initial velocity travel in semicircular orbits in the magnetic field B. The partides are accelerated to higher speeds each time they pass through the gap between the metal "dees," where there is an electric field E. (There is no electric field inside the hollow metal dees where the protons move in circular paths.) The electric field changes direction each half- cycle, owing to an ac voltage V-Vasin2rft, so that the particles are increased in speed at each passage through the gap. (a) Show that the frequency of the voltage must be f - Bq/2mm, where is the charge on the particles and their mass. (b) Show that the kinetic energy of the particles increases by 24V, each revolution, assuming that the gap is small. (c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons In MAV? Figure 27-55 "Dees" B Gap