A particle of charge per unit mass $\alpha$ is released from origin with velocity $\overrightarrow{\mathrm{v}}={\overrightarrow{\mathrm{v}}}_0\widehat{\mathrm{i}}$ in a magnetic field

$\begin{array}{l}\overrightarrow{\mathrm{B}}=-{\mathrm{B}}_0\widehat{\mathrm{k}}\mathrm{for}\mathrm{x}\le \frac{\sqrt{3}}{2}\frac{{\mathrm{v}}_0}{{\mathrm{B}}_0\mathrm{\alpha }}\\ \mathrm{and}\overrightarrow{\mathrm{B}}=0\mathrm{for}\mathrm{x}>\frac{\sqrt{3}}{2}\frac{{\mathrm{v}}_0}{{\mathrm{B}}_0\mathrm{\alpha }}\end{array}$

The x-coordinates of the particle at time $\mathrm{t}\left(>\frac{\mathrm{\pi }}{3{\mathrm{B}}_0\mathrm{\alpha }}\right)$ would be

• A

  $\frac{\sqrt{3}}{2}\frac{{\mathrm{v}}_0}{{\mathrm{B}}_0\mathrm{\alpha }}+\frac{\sqrt{3}}{2}{\mathrm{v}}_0\left(\mathrm{t}-\frac{\mathrm{\pi }}{{\mathrm{B}}_0\mathrm{\alpha }}\right)$

• B

  $\frac{\sqrt{3}}{2}\frac{{\mathrm{v}}_0}{{\mathrm{B}}_0\mathrm{\alpha }}+{\mathrm{v}}_0\left(\mathrm{t}-\frac{\mathrm{\pi }}{{\mathrm{B}}_0\mathrm{\alpha }}\right)$

• C

  $\frac{\sqrt{3}}{2}\frac{{\mathrm{v}}_0}{{\mathrm{B}}_0\mathrm{\alpha }}+\frac{{\mathrm{v}}_0}{2}\left(\mathrm{t}-\frac{\mathrm{\pi }}{3{\mathrm{B}}_0\mathrm{\alpha }}\right)$

• D

  $\frac{\sqrt{3}}{2}\frac{{\mathrm{v}}_0}{{\mathrm{B}}_0\mathrm{\alpha }}+\frac{{\mathrm{v}}_0\mathrm{t}}{2}$