Cyclotron Period and Frequency
For perpendicular non-relativistic motion in uniform B, angular frequency omega_c = |q|B/m, period T = 2pi m/(|q|B), and frequency f = |q|B/(2pi m).
Why this shows up in the exam
Finding return time to the starting point · Comparing isotope revolution frequencies · Setting cyclotron oscillator frequency
Learn the idea
The non-relativistic orbital period in uniform B depends on mass and charge, not on radius or speed. As a particle speeds up, its circle grows in exactly the way needed to keep one revolution taking the same time. That cancellation is the timing idea behind cyclotron resonance.
🧠 Memory hook: The orbit grows, but the clock stays the same.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- omega_c = |q| B/m — cyclotron angular frequency
- T = 2 pi m/(|q| B) — orbital period independent of speed in the non-relativistic regime
- f = |q| B/(2 pi m) — revolution frequency
How to approach it
- 1Decide what fraction of a revolution is required
- 2Use T = 2pi m/(|q|B)
- 3Check whether the non-relativistic assumption is valid
Common slip-ups that cost marks
- •Using half a period for first return to the original point
- •Including speed in T
- •Ignoring relativistic failure at very high energy
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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