A uniform electric field of strength $\;\overrightarrow{E}\;$ exists in a region . An electron enters a point $A$ with velocity $v$ as shown . It moves through the electric field and reaches at point $B$ . Velocity of particle at $B$ is $2v$ at $30^{\circ}\;$ with x - axis . Then electric field $\;\overrightarrow{E}\;$ is

Question

$(a)\;\large\frac{3 m_{e}v^2}{2ea}\qquad(b)\;-\large\frac{3 m_{e}v^2}{2ea}\qquad(c)\;\large\frac{ m_{e}v^2}{2ea}\qquad(d)\;-\large\frac{ m_{e}v^2}{2ea}$