SATHEE: moving-charges-and-magnetism Question 27

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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

$\vec{F} = q (\vec{v} \times \vec{B})$

$∴$ Centripetal force, $\frac{m v^{2}}{r} = q v B_{⊥}$

$\begin{aligned} or, & r & = \frac{m v}{q B_{⊥}} & 1 / 2 ∴ & Frequency, f & = \frac{v}{2 π r} = \frac{q B_{⊥}}{2 π m} & 1 / 2 \end{aligned}$

Hence, it is independent of the velocity or the energy of the particle.

[CBSE Marking Scheme 2014]

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