A particle of specific charge $π C/kg,$ is projected with a speed u from origin along positive direction of x-axis. There exists a magnetic field $\vec{B} = 1 (- \hat{k})$ Tesla in the region. Choose the correct option(s).

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Deviation suffered by the particle after 1/3 sec is $π/ 3$ radians.

Time after which it touches the x-axis for the first time is 4 sec.

Velocity of the particle after 1/6 sec of projection is $\frac{\sqrt{3} u}{2} \hat{i} + \frac{u}{2} \hat{j}$

Deviation suffered by the particle after 1/2 sec is $π/ 4$ radians.

answer is C, D.

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Detailed Solution

$\begin{array}{l} T = \frac{2 π m}{B q} = 2 \sec \\ 2 \sec \to 2 π \\ After 1 / 2 \sec \to π / 2 deviation \\ After 1 / 3 \sec \to π / 3 deviation \\ After 1 / 6 \sec \to π / 6 deviation \\ \Rightarrow \vec{v} = u \cos \frac{π}{6} \hat{i} + u \sin \frac{π}{6} \hat{j} = \frac{\sqrt{3}}{2} u \hat{i} + \frac{u}{2} \hat{j} \end{array}$