A charged particle of specific charge $α$ is released from origin at time t = 0 with velocity $\vec{V} = V_{o} \hat{i} + V_{o} \hat{j}$ in magnetic field $\vec{B} = B_{0} \hat{i}$ . The coordinates of the particle at time $t = \frac{π}{B_{0} α}$ are (specific charge $α$ = q/m)

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$(\frac{V_{0}}{2 B_{0} α}, \frac{\sqrt{2} V_{0}}{{αB}_{0}}, \frac{- V_{0}}{B_{0} α})$

$(\frac{- V_{o}}{2 B_{0} α}, 0, 0)$

$(0, \frac{2 V_{0}}{B_{0} α}, \frac{V_{0} π}{2 B_{0} α})$

$(\frac{V_{0} π}{B_{0} α}, 0, - \frac{2 V_{0}}{B_{0} α},)$

answer is D.

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Detailed Solution

The path is helical and the time is half of the time period. So the particle completes half a round(in yz plane) and goes in the x direction with a speed v. It covers two times the radius of the helix in z direction and half of the pitch in x direction and nothing in y direction. Hence D.

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