A charged particle of specific charge $\alpha$  is released from origin at time t = 0 with velocity $\overrightarrow{V}={\text{V}}_{\text{0}}\hat{i}+{\text{V}}_{\text{0}}\hat{j}$ in magnetic field $\overrightarrow{B}={\text{B}}_{\text{0}}\hat{i}$ . The co-ordinates of the particle at time$\text{t}=\frac{\pi }{{\text{B}}_{\text{0}}\alpha }$  are (specific charge$\alpha =\frac{\text{q}}{\text{m}}$ )

Specific charge $=\alpha$

$\overrightarrow{V}={\text{V}}_{\text{0}}\hat{i}+{\text{V}}_{\text{0}}\hat{j}$  

$\overrightarrow{B}={\text{B}}_{\text{0}}\hat{i}$

$\text{t}=\frac{\pi }{B_0\alpha }=\frac{\text{T}}{\text{2}}$

$\overrightarrow{F}=q\left(\overrightarrow{V}\times \overrightarrow{B}\right)$

$=\text{q}\left[\left({\text{V}}_0\hat{i}+{\text{V}}_{\text{0}}\hat{j}\right)\times {\text{B}}_0\hat{i}\right]$

$={\text{qV}}_{\text{0}}{\text{B}}_{\text{0}}\hat{k}$

$\therefore$ There is no force along x and y – axis

$\Rightarrow \overrightarrow{a}=\alpha {\text{V}}_{\text{0}}{\text{B}}_{\text{0}}\hat{k}\left[\frac{\text{q}}{\text{m}}=\alpha \right]$

The particle completes vertical semi circle in x – z plane

X – co-ordinate x = vt

$x=\frac{{\text{V}}_0\pi }{{\text{B}}_{\text{0}}\alpha }$

Y – co-ordinate y = 0

Z – co-ordinate $\text{z}=-2\text{r}$

${\text{z}}^2=-2\left(\frac{{\text{mV}}_{\text{0}}}{\text{Bq}}\right)=-2\left(\frac{{\text{V}}_{\text{0}}}{{\text{B}}_{\text{0}}\alpha }\right)$

$\left(x,y,z\right)=\left(\frac{{\text{V}}_{\text{0}}\pi }{\text{B}\alpha },0,\frac{-2{\text{V}}_{\text{0}}}{B_0\alpha }\right)$