(7%) Problem 2: Consider an experimental setup where charged particles (electron

Question

(7%) Problem 2: Consider an experimental setup where charged particles (electrons or protons) are first accelerated by an electric field and then injected into a region of constant magnetic field with a field strength of 0.45 T. 33% Part (a) what is the potential difference, in volts, required in the first part of the experiment to accelerate electrons to a speed of 59 107 m /s? × 33% Part (b) Find the radius of curvature in meters. of the path of a proton accelerated through this same potential after the proton crosses into the region with the magnetic field. 33% Part ) What is the ratio of the radius of curvatures for a proton an an electron traveling through this apparatus? Grade Summary Deductions Potential 0% 100%

Explanation / Answer

a) work done through potential difference is change in kinetic energy

q*dV = 0.5*m*V^2

q is the magnitude of charge = 1.6*10^-19 C

dV = ?

m is the mass of the electron = 9.11*10^-31 Kg

then

q*dv = 0.5*m*v^2

(1.6*10^-19*dV) = 0.5*9.11*10^-31*(5.9*10^7)^2

dV = 9910 V

b) radius of curvature is r = (m*v)/(q*B)

m is the mass of the proton = 1.67*10^-27 kg

q is the charge on proton

then

r = (m*v)/(q*B) =(1.67*10^-27*5.9*10^7)/(1.6*10^-19*0.45) = 1.368 m

C) rp/re

re = (m*v)/(q*B) = (9.11*10^-31*5.9*10^7)/(1.6*10^-19*0.45)

re = 7.46*10^-4 m

then

rp/re = (1.368)/(7.46*10^-4) = 1833.78

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