$A$ particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v} = (\frac{v_0}{\sqrt{2}}\hat{i} + \frac{v_0}{\sqrt{2}}\hat{j})$. There exists a uniform magnetic field $\vec{B} = B_0\hat{z}$ and a space varying electric field $\vec{E} = E_0 e^{-\lambda x}\hat{x}$ within the region $0 \leq x \leq L$. After travelling a distance such that $x$-coordinate has changed from $x = 0$ to $x = L$, the change in the kinetic energy is . . . . . . .

• A
  $\frac{qE_0}{\lambda}[1 - e^{-\lambda L}]$
• B
  $(\frac{v_0 q B_0}{2\lambda}) [2 - e^{-2\lambda L}]$
• C
  $\frac{qE_0}{\lambda}[1 + e^{-\lambda L}]$
• D
  $q(\frac{E_0 + v_0 B_0}{\lambda})[1 - e^{-\lambda L/2}]$