Two small spheres each of mass $10 \mathrm{mg}$ are suspended from a point by threads $0.5 \mathrm{m}$ long. They are equally charged and repel each other to a distance of $0.20 \mathrm{m}$. The charge on each of the sphere is $\frac{a}{21}\times {10}^{-8} \mathrm{C}.$ The value of $a$ will be ___.[Given $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q$. The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2}L$

Given below are two statements
Statement $\mathrm{I}$ : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere.

Statement $\mathrm{II}$ : If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at any point on the spherical surface of radius $r\left(<R\right)$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not

In the light of the above statements, choose the correct answer from the options given below:

A charged particle (mass $\mathrm{m}$ and charge $\mathrm{q}$) moves along $\mathrm{X}$ axis with velocity ${\mathrm{V}}_0$. When it passes through the origin it enters a region having uniform electric field $\overrightarrow{\mathrm{E}}=-\mathrm{E}\hat{\mathrm{j}}$ which extends upto $\mathrm{x}=\mathrm{d}$. Equation of path of electron in the region $\mathrm{x}>\mathrm{d}$ is: