


Due to the presence of the current $I_1$ at the origin
$(A)$ If $\theta=0^{\circ}$, the charge moves in a circular path in the $x-z$ plane.
$(B)$ If $\theta=0^{\circ}$, the charge undergoes helical motion with constant pitch along the $y$-axis.
$(C)$ If $\theta=10^{\circ}$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis.
$(D)$ If $\theta=90^{\circ}$, the charge undergoes linear but accelerated motion along the $y$-axis.
Figure: $Image$
$(A)$ The particle enters Region $III$ only if its velocity $V>\frac{q / B}{m}$
$(B)$ The particle enters Region $III$ only if its velocity $\mathrm{V}<\frac{\mathrm{q} / \mathrm{B}}{\mathrm{m}}$
$(C)$ Path length of the particle in Region $II$ is maximum when velocity $V=\frac{q / B}{m}$
$(D)$ Time spent in Region $II$ is same for any velocity $V$ as long as the particle returns to Region $I$