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Problem 2: A 5.0-mm-diameter proton beam carries a total current of I = 1.5 mA. The current density in the proton beam, which increases with distance from the center, is given by J = Jedge (r/R), where R is the radius of the beam and Jedge is the current density at the edge. Determine the value of Jedge. a) Fig. 3 shows the cross section of the beam. Compute the current dI flowing through the ring of radius r and width dr shown in the figure. Notice that for small dr the area of the ring can be approximated by the area of a rectangle that you can get by "unrolling" the ring. dr I = = f dI. Express Jedge as a function of I and R and compute its value. 2ПГ c) How many protons per second are delivered by this proton beam? R b) Sum up the contributions from all rings by integrating dI with respect to the radial coordinate r, r=R FIG. 3: The scheme for Problem 2

Problem 2: A 5.0-mm-diameter proton beam carries a total current of I = 1.5 mA. The current density in the proton beam, which increases with distance from the center, is given by J = Jedge (r/R), where R is the radius of the beam and Jedge is the current density at the edge. Determine the value of Jedge. a) Fig. 3 shows the cross section of the beam. Compute the current dI flowing through the ring of radius r and width dr shown in the figure. Notice that for small dr the area of the ring can be approximated by the area of a rectangle that you can get by "unrolling" the ring. dr I = = f dI. Express Jedge as a function of I and R and compute its value. 2ПГ c) How many protons per second are delivered by this proton beam? R b) Sum up the contributions from all rings by integrating dI with respect to the radial coordinate r, r=R FIG. 3: The scheme for Problem 2

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Hello, can you help me with me with part a, part b and part c, and can you label which one is one, thank you so much

Problem 2: A 5.0-mm-diameter proton beam carries a total current of I = 1.5 mA. The current density in the proton beam, which increases with distance from the center, is given by J = Jedge (r/R), where R is the radius of the beam and Jedge is the current density at the edge. Determine the value of Jedge. a) Fig. 3 shows the cross section of the beam. Compute the current dI flowing through the ring of radius r and width dr shown in the figure. Notice that for small dr the area of the ring can be approximated by the area of a rectangle that you can get by "unrolling" the ring. dr I = = f dI. Express Jedge as a function of I and R and compute its value. 2ПГ c) How many protons per second are delivered by this proton beam? R b) Sum up the contributions from all rings by integrating dI with respect to the radial coordinate r, r=R FIG. 3: The scheme for Problem 2
Transcribed Image Text:Problem 2: A 5.0-mm-diameter proton beam carries a total current of I = 1.5 mA. The current density in the proton beam, which increases with distance from the center, is given by J = Jedge (r/R), where R is the radius of the beam and Jedge is the current density at the edge. Determine the value of Jedge. a) Fig. 3 shows the cross section of the beam. Compute the current dI flowing through the ring of radius r and width dr shown in the figure. Notice that for small dr the area of the ring can be approximated by the area of a rectangle that you can get by "unrolling" the ring. dr I = = f dI. Express Jedge as a function of I and R and compute its value. 2ПГ c) How many protons per second are delivered by this proton beam? R b) Sum up the contributions from all rings by integrating dI with respect to the radial coordinate r, r=R FIG. 3: The scheme for Problem 2
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