Question 156 of 276

A charged particle of mass ‘ $m$ ’ and charge ‘ $q$ ’ moving under the influence of uniform electric field $\vec{\text{E}}\hat{i}$ and a uniform magnetic field $\vec{\text{B}}\hat{k}$ follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, $v\vec{i}$ and $-2v\vec{j}$ . Then which of the following statements (A, B, C, D) are the correct? (Trajectory shown is schematic and not to scale)



$\left(A\right)$ $E=\dfrac{3}{2}\left(\dfrac{m{v}^{2}}{qa}\right)$
$\left(B\right)$ Rate of work done by the electric field at P is $\dfrac{3}{2}\left(\dfrac{m{v}^{3}}{a}\right)$
$\left(C\right)$ Rate of work done by both the fields at Q is zero
$\left(D\right)$ The difference between the magnitude of angular momentum of the particle at P and Q is $2mav$ .