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

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

Solution

$\mathrm{Bqv}=\frac{\mathrm{mv}^{2}}{\mathrm{R}} \quad \therefore \mathrm{R}=\frac{\mathrm{mv}}{\mathrm{qB}}$ $\frac{1}{2} \mathrm{mv}_{2}^{2}=3 \times \frac{1}{2} \mathrm{mv}_{1}^{2}$ $\therefore \mathrm{v}_{2}=\sqrt{3} \mathrm{v}_{1}$ $\therefore \quad \mathrm{R}_{2}=\frac{\sqrt{3} \mathrm{mv}}{\mathrm{q} \mathrm{B}}=\sqrt{3} \mathrm{R}$

Asked in: MHT CET 2020 (16 Oct Shift 1)

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