CH27HW sessicnn CH27 HWProblem 27.73 Problem 27.73 Part A A 56-mm-diameter proto

Question

CH27HW sessicnn CH27 HWProblem 27.73 Problem 27.73 Part A A 56-mm-diameter proton beam carries a tolal current of 1.1 mA The curent density in the proton beam which increases with distance from the center, tS given by J= J-le(r/R),where Ris the raius of the beam and Jedge is the current density at the edge How many prolons per second a Express your answer using tw Submit My Answers Gve! Part B Determine the value of Jage Express your answer to two signif | Value Uni My Answers Give Up Submit O Type here to search o e @

Explanation / Answer

A) protons per second = 1.1e-3/(1.6e-19)

= 6.9*10^15 protons per sec. answer

B)total current i = integral J 2pi r dr= integral Jedge*(r/R)* 2 pi r dr

= 2pi*Jedge/R *r^3/3

= 2 pi Jedge R^2/3

1.1e-3 = 2 pi Jedge*2.8e-3^2/3

Jedge = 3*1.1e-3/(2pi*2.8e-3^2)

= 67 A/m^2 answer

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