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Moving Charges and Magnetism
Motion of Charge in Magnetic Field: Cyclotron Frequency
1 question from 1 paper, each with its answer.
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Concepts tested
- Frequency independent of speed
All Questions
2001 AIPMT 1 question
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An electron having mass 'm' and kinetic energy E enters in uniform magnetic field B perpendicularly, then its frequency will be : -The magnetic force provides the centripetal force: $evB = \dfrac{mv^2}{r} \Rightarrow r = \dfrac{mv}{eB}$
Time period: $T = \dfrac{2\pi r}{v} = \dfrac{2\pi m}{eB}$
Frequency: $f = \dfrac{1}{T} = \dfrac{eB}{2\pi m}$
The frequency does not depend on the speed or kinetic energy E of the electron; only the radius does.
(The expression $\dfrac{2\pi m}{eB}$ is the time period, not the frequency.)