The magnetic poles of a small cyclotron produce a magnetic field with magnitude
ID: 2261632 • Letter: T
Question
The magnetic poles of a small cyclotron produce a magnetic field with magnitude 0.75 T. The poles have a radius of 0.39 m, which is the maximum radius of the orbits of the accelerated particles. (a) What is the maximum energy to which protons (q = 1.60 10-19 C, m = 1.67 10-27 kg) can be accelerated by this cyclotron? Give your answer in joules and electron volts.J
eV
(b) What is the time for one revolution of a proton orbiting at this maximum radius?
s
(c) What would the magnetic field magnitude have to be for the maximum energy to which a proton can be accelerated to be twice that calculated in part (a)?
T
(d) For B = 0.75 T, what is the maximum energy to which alpha particles (q = 3.20 10-19 C, m = 6.65 10-27 kg) can be accelerated by this cyclotron?
J
How does this compare to the maximum energy for protons?
(maximum energy for alpha particles / maximum energy for protons) = The magnetic poles of a small cyclotron produce a magnetic field with magnitude 0.75 T. The poles have a radius of 0.39 m, which is the maximum radius of the orbits of the accelerated particles. (a) What is the maximum energy to which protons (q = 1.60 10-19 C, m = 1.67 10-27 kg) can be accelerated by this cyclotron? Give your answer in joules and electron volts.
J
eV
(b) What is the time for one revolution of a proton orbiting at this maximum radius?
s
(c) What would the magnetic field magnitude have to be for the maximum energy to which a proton can be accelerated to be twice that calculated in part (a)?
T
(d) For B = 0.75 T, what is the maximum energy to which alpha particles (q = 3.20 10-19 C, m = 6.65 10-27 kg) can be accelerated by this cyclotron?
J
How does this compare to the maximum energy for protons?
(maximum energy for alpha particles / maximum energy for protons) = The magnetic poles of a small cyclotron produce a magnetic field with magnitude 0.75 T. The poles have a radius of 0.39 m, which is the maximum radius of the orbits of the accelerated particles. (a) What is the maximum energy to which protons (q = 1.60 10-19 C, m = 1.67 10-27 kg) can be accelerated by this cyclotron? Give your answer in joules and electron volts.
J
eV
(b) What is the time for one revolution of a proton orbiting at this maximum radius?
s
(c) What would the magnetic field magnitude have to be for the maximum energy to which a proton can be accelerated to be twice that calculated in part (a)?
T
(d) For B = 0.75 T, what is the maximum energy to which alpha particles (q = 3.20 10-19 C, m = 6.65 10-27 kg) can be accelerated by this cyclotron?
J
How does this compare to the maximum energy for protons?
(maximum energy for alpha particles / maximum energy for protons) = (a) What is the maximum energy to which protons (q = 1.60 10-19 C, m = 1.67 10-27 kg) can be accelerated by this cyclotron? Give your answer in joules and electron volts.
J
eV
(b) What is the time for one revolution of a proton orbiting at this maximum radius?
s
(c) What would the magnetic field magnitude have to be for the maximum energy to which a proton can be accelerated to be twice that calculated in part (a)?
T
(d) For B = 0.75 T, what is the maximum energy to which alpha particles (q = 3.20 10-19 C, m = 6.65 10-27 kg) can be accelerated by this cyclotron?
J
How does this compare to the maximum energy for protons?
(maximum energy for alpha particles / maximum energy for protons) =
Explanation / Answer
B = 0.75 T
r = 0.39 m
q = 1.6*10^-19 C
m = 1.67*10^-27 kg
a) r = m*v/B*q
v = B*q*r/m
KE = 0.5*m*v^2
= 0.5*m*B^2*q^2*r^2/m^2
= 0.5*B^2*q^2*r^2/m
= 6.557*10^-13 J
= 6.557*10^-13/1.6*10^-19
= 4.098*10^6 e Volts
b)
T = 2*pi*m/(B*q) = 2*3.14*1.67*10^-27/(0.75*1.6*10^-19) = 8.74*10^-8 s
c)
r = m*v/(B*q)
r1/r2 = B2/B1
B2 = (r1/r2)*B1 = (1/2)*0.75 = 0.375 T
d)
KE = 0.5*m*v^2
= 0.5*m*B^2*q^2*r^2/m^2
= 0.5*B^2*q^2*r^2/m
= 6.587*10^-13 J
KE_alfa/KE_proton = 1
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