A cyclotron in a magnetic field of 8.61 T is used to accelerate protons to 49.9

Question

A cyclotron in a magnetic field of 8.61 T is used to accelerate protons to 49.9 % of the speed of light.

a) What is the cyclotron frequency of these protons?


b) What is the radius of their trajectory in the cyclotron?


c) What is the cyclotron frequency of the same protons in the Earth's magnetic field? Assume that the Earth's magnetic field is about 0.481 G

d) What is the trajectory radius of the same protons in the Earth's magnetic field? Assume that the Earth's magnetic field is about 0.481 G.

Explanation / Answer

part 1-

frequency f is given by

f = Bq/2m

B = 8.61T

q = 1.6 x 10-19

m = 1.67 x 10-27

f=2.51 x 108 Hz

part 2

mv2/r = qvB

v = 0.499 x 3 x 108 m/s

r= mv/qB

=0.181m

part 3

f = Bq/2m

B = 0.481T

part 4

mv2/r = qvB

B = 0.481T

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.