A large metal plate has a surface charge density of $8.85\times {10}^{-6} \mathrm{C} {\mathrm{m}}^{-2}$. An electron having initial kinetic energy of $8\times {10}^{-17} \mathrm{J}$ is moving towards the center of the plate. If the electron stops just before reaching the plate then the initial distance between the electron and the plate is [Take ${\epsilon }_0=8.85\times {10}^{-12} {\mathrm{C}}^2 \mathrm{N} {\mathrm{m}}^{-2}$]

Define electric dipole moment. An electric dipole is placed within a uniform electric field $\left(\mathrm{E}\right)$ and is rotated to an angle $\theta =180°$. Find out the work done.

The diagrams below show regions of equipotential.



A positive charge is moved from $A$ to $B$ in each diagram.

A point particle of mass $0.5 \mathrm{kg}$ is moving along the $X$ -axis under a force described by the potential energy $V$ shown below. It is projected towards the right from the origin with a speed $v$.

What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

A two point charges $4q$ and $–q$ are fixed on the $x$ -axis at $x=\frac{-d}{2}$ and $x=\frac{d}{2}$, respectively. If the third point charge ‘$q$ ’ is taken from the origin to $x=d$ along the semicircle as shown in the figure, the energy of the charge will: