Physics - Magnetism Question with Solution | TestHub

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



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