A charged particle when enters a uniform magnetic field moves in a helical path. If its angular velócity is…

A charged particle when enters a uniform magnetic field moves in a helical path. If its angular velócity is $4 \pi \times 10^6$ rads $^{-1}$ and its velocity in the direction of magnetic field is $3 \times 10^5 \mathrm{~ms}^{-1}$ then the pitch of the helix is
  1. $5 \mathrm{~cm}$
  2. $10 \mathrm{~cm}$
  3. $15 \mathrm{~cm}$
  4. $20 \mathrm{~cm}$

Solution

Angular velocity, $\omega=4 \pi \times 10^6 \mathrm{rad} / \mathrm{s}$ Velocity of changes particle, $v=3 \times 10^5 \mathrm{~m} / \mathrm{s}$ Pitch of the helix $=\mathrm{v} \times \mathrm{t}$ $=3 \times 10^5 \times \frac{2 \pi}{\omega}$ $\begin{aligned} & =3 \times 10^5 \times \frac{2 \pi}{4 \pi \times 10^6} \\ & =15 \mathrm{~cm}\end{aligned}$

Asked in: AP EAMCET 2023 (16 May Shift 1)

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