GRE Physics GR 1777 Problem Solution
021. Electrodynamics (Cyclotron)
Solution
The cyclotron frequency is the frequency of a charged particle moving perpendicular to the direction of a constant magnetic field B.
Since the motion of a charged particle in the cyclotron is circular (because of a uniform magnetic field), we can calculate the cyclotron frequency by using the fact that the centripetal force equals the magnetic Lorentz force.
The above equation yields
Thus,
Now, let\’s look at the particles, Mass: $latex m_p : m_d : m_\\alpha = 1 : 2 : 4$ Electric charge: $latex q_p : q_d : q_\\alpha : 1 : 1 : 2$
Therefore, their cyclotron frequencies in the same magnetic field,
Answer
(E) $latex \\omega_p > \\omega_d = \\omega_\\alpha$
References
https://en.wikipedia.org/wiki/Cyclotron_resonance http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/cyclot.html
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