A charged particle is moving in a uniform magnetic field in a circular path of radius ' $R$ '. When the…

A charged particle is moving in a uniform magnetic field in a circular path of radius ' $R$ '. When the kinetic energy of the particle is increased to three times, then the new radius will be
  1. $\frac{\mathrm{R}}{3}$
  2. $\frac{\mathrm{R}}{\sqrt{3}}$
  3. $\quad \sqrt{3} \cdot \mathrm{R}$
  4. $3 \cdot \mathrm{R}$

Solution

$\begin{aligned} & \quad \text { Radius, } r=\frac{\sqrt{2 m K}}{q B} \Rightarrow r \propto \sqrt{K} \\ & \therefore \quad \\ & \quad \frac{R}{R_2}=\sqrt{\frac{K}{3 K}} \\ & \\ & \Rightarrow R_2=\sqrt{3} R\end{aligned}$

Asked in: MHT CET 2024 (10 May Shift 2)

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