$A$ charged particle of mass $m$ and charge $q$ moving under the influence of a uniform electric field $E\hat{i}$ and a uniform magnetic field $B\hat{k}$ follows a trajectory from point $P$ to $Q$ as shown in the figure. The velocities at $P$ and $Q$ are respectively $v\hat{i}$ and $-2v\hat{j}$. Which of the following statements $(A, B, C, D)$ are correct? (Trajectory shown is schematic and not to scale)
$(A)$ $E = \frac{3}{4}\left(\frac{mv^{2}}{qa}\right)$
$(B)$ Rate of work done by the electric field at $P$ is $\frac{3}{4}\left(\frac{mv^{3}}{a}\right)$
$(C)$ Rate of work done by both the fields at $Q$ is zero
$(D)$ The difference between the magnitude of angular momentum of the particle at $P$ and $Q$ is $2mav$.

• A
  $(A), (B), (C), (D)$
• B
  $(A), (B), (C)$
• C
  $(B), (C), (D)$
• D
  $(A), (C), (D)$