Two identical conducting spheres with negligible volume have $2.1 \mathrm{nC}$ and $-0.1 \mathrm{nC}$ charges, respectively. They are brought into contact and then separated by a distance of $0.5 \mathrm{m}$. The electrostatic force acting between the spheres is ___$\times {10}^{-9} \mathrm{N}$.
[Given : $4\pi {\epsilon }_0=\frac{1}{9\times {10}^9}$ SI unit]

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:

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass ? (Curves are drawn schematically and are not to scale)

A charge Q is distributed over two concentric conducting thin spherical shells radii $\mathrm{r}$ and $\mathrm{R} \left(\mathrm{R}>\mathrm{r}\right)$. If the surface charge densities on the two shells are equal, the electric potential at the common centre is :