In a certain region of space, there exists a uniform and constant electric field of strength E along x-axis and uniform constant magnetic field of induction B along z-axis. A charged particle having charge q and mass m is projected with speed v parallel to x-axis from a point (a, b, 0). When the particle reaches a point $\left(2\mathrm{a},\frac{\mathrm{b}}{2},0\right)$ its speed becomes 2v. Find the value of electric field strength.

• A

  $\frac{3}{2}\frac{{\mathrm{mv}}^2}{\mathrm{qa}}$

• B

  $\frac{{\mathrm{mv}}^2}{qB}$

• C

  $\frac{2{\mathrm{mv}}^2}{qBa}$

• D

  $\frac{3}{2}\text{\hspace{0.17em}\hspace{0.17em}vB}$