Q. A particle of charge per unit mass α is released from origin with velocity $ \displaystyle \vec{v} = v_0\hat{i} $ in a magnetic field $\displaystyle \vec{B}= B_0\hat{k}$ for $\displaystyle x \leq \frac{\sqrt 3}{2} \frac{ v_0 }{ B_0 \alpha } $ and B_{0} = 0 for $ \displaystyle x \geq \frac{\sqrt 3}{2} \frac{ v_0 }{ B_0 \alpha } $ . The x-coordinate of the particle at time $ \Large t > (\frac{\pi}{3 B_0 \alpha})$ would be

(a) $ \displaystyle \frac{\sqrt 3}{2} \frac{ v_0 }{ B_0 \alpha } + \frac{\sqrt 3v_0}{2} (t – \frac{\pi }{ B_0 \alpha })$

(b) $ \displaystyle \frac{\sqrt 3}{2} \frac{ v_0 }{ B_0 \alpha } + v_0 (t – \frac{\pi }{ 3 B_0 \alpha })$

(c) $ \displaystyle \frac{\sqrt 3}{2} \frac{ v_0 }{ B_0 \alpha } + \frac {v_0}{2} (t – \frac{\pi }{ 3 B_0 \alpha })$

(d) $ \displaystyle \frac{\sqrt 3}{2} \frac{ v_0 }{ B_0 \alpha } + \frac {v_0 t}{2} $

Ans: (c)