Q 12-04-036JEE MainJEE Main 2026 (8 Apr, Shift 2)Medium
A $5$ mg particle carrying a charge of $5\pi \times 10^{-6}$ C is moving with velocity of $(3\hat{i} + 2\hat{k}) \times 10^{-2}$ m/s in a region having magnetic field $\vec{B} = 0.1\hat{k}\ \text{Wb/m}^2$. It moves a distance of $\alpha$ meter along $\hat{k}$ when it completes $5$ revolutions. The value of $\alpha$ is ______.
Numerical value type. Enter your answer.
Answer: 2
Concept. Helix along $\vec B=B\hat k$: the $\hat k$ component of velocity is unchanged, and each turn takes $T=\dfrac{2\pi m}{qB}$.
Step 1. Period. $T=\dfrac{2\pi\times5\times10^{-6}}{5\pi\times10^{-6}\times0.1}=20$ s.
Step 2. Distance. $5T=100$ s; $2\times10^{-2}\times100=2$ m.
Answer. $\alpha=2$.
Solution by Sreeraj P, M.Sc Physics
