A particle of specific charge $\text{'}\alpha \text{'}$ is projected from origin at t=0 with a velocity $\overrightarrow{v}=v_0(\widehat{i}+\widehat{k})$ in a magnetic field $\overrightarrow{B}=-B_0\widehat{k.}$ Then ( mass of particle = 1 unit)

Time period of the motion is , $T=\frac{2\pi m}{Bq}=\frac{2\pi }{\alpha B_0}$

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

Velocity of the particle is $-V_0\widehat{i}-V_0\widehat{k}$.

Speed of charge in magnetic field always remains Constant So it will be $V=V_0\sqrt{2}$

At $t=\frac{2\pi }{\alpha B_0}=T$

Displacement is equal to pitch which is given as

$\Delta x=V_{0}T=\frac{2\pi v_o}{\alpha B_0}$

At $t=\frac{2\pi }{\alpha B_0}=T$

Distance is given as, $\Delta x=V\times T=\frac{2\sqrt{2}{v}_0\pi }{\alpha B_0}$.