• # question_answer A charged particle of specific charge (charge/mass) a is the projected from origin with a velocity $\vec{u}={{v}_{0}}(\hat{i}+\hat{j})$ in a uniform and constant magnetic field $\vec{B}={{B}_{0}}\hat{i}.$ The position co-ordinates of the particle at time $t=\frac{\pi }{{{B}_{0}}\alpha }$ are - A) $\left( \frac{{{v}_{0}}}{2{{B}_{0}}\alpha },\frac{\sqrt{2}{{v}_{0}}}{\alpha {{B}_{0}}},\frac{-{{v}_{0}}}{{{B}_{0}}\alpha } \right)$ B) $\left( -\frac{{{v}_{0}}}{2{{B}_{0}}\alpha },0,0 \right)$ C) $\left( 0,\frac{2{{v}_{0}}}{{{B}_{0}}\alpha },\frac{{{v}_{0}}\pi }{2{{B}_{0}}\alpha } \right)$ D) $\left( \frac{{{v}_{0}}\pi }{{{B}_{0}}\alpha },0,\frac{-2{{v}_{0}}}{{{B}_{0}}\alpha } \right)$

[D] Radio of projection of helix will be $r=\frac{{{v}_{0}}}{\alpha {{B}_{0}}}$ and time period of projection will be $T=\frac{2\pi }{\alpha {{B}_{0}}},$ projected circle will be formed on $y-z$ plane. It will make half circle in time $t=\frac{\pi }{{{B}_{0}}\alpha }.$ x-coordinate = ${{v}_{0}}t={{v}_{0}}.\frac{\pi }{{{B}_{0}}\alpha }.$