A charged particle of mass ' m ' and charge 'q' moving under the influence of uniform electric field E i and a uniform magnetic field B k follows a…

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

$\displaystyle \mathrm{E}=\frac{3}{4}\left(\frac{\mathrm{~m} v^2}{\mathrm{qa}}\right)$

Rate of work done by the electric field at P is $\displaystyle \frac{3}{4}\left(\frac{\mathrm{~m} v^3}{\mathrm{a}}\right)$

Rate of work done by both the fields at Q is zero

The difference between the magnitude of angular momentum of the particle at P and Q is $\displaystyle 2$ mav.