Question: Q. 5. Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.
U [O.D. I, II, III 2014]
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Solution:
Ans. When a particle of mass $m$ and charge $q$, moves with a velocity $v$, in a uniform magnetic field $B$, it experiences a force $F$ where
$$ \vec{F}=q(\vec{v} \times \vec{B}) $$
$\therefore$ Centripetal force, $\frac{m v^{2}}{r}=q v \mathrm{~B}_{\perp}$
$$ \begin{aligned} \text { or, } & r & =\frac{m v}{q B_{\perp}} & 1 / 2 \ \therefore & \text { Frequency, } f & =\frac{v}{2 \pi r}=\frac{q B_{\perp}}{2 \pi m} & 1 / 2 \end{aligned} $$
Hence, it is independent of the velocity or the energy of the particle.
[CBSE Marking Scheme 2014]
