Two point charges of $12\ \mu C$ and $8\ \mu C$ are placed $10\ cm$ apart. The work done in bringing them $4\ cm$ closer is:

$A$ test charge $q$ is moved in the electric field of a point charge $Q$ along two different closed paths as shown in the figure. The first path has sections along and perpendicular to the lines of the electric field. The second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases?

$A$ particle of mass $1 \text{ g}$ and charge $1 \mu\text{C}$ is held at rest on a frictionless horizontal surface at a distance of $1 \text{ m}$ from a fixed charge of $2 \text{ mC}$. If the particle is released, it will be repelled. What is the speed of the particle when it is at a distance of $10 \text{ m}$ from the fixed charge (in $\text{ m s}^{-1}$)?

Explain electric potential energy. Show that the sum of kinetic energy and electric potential energy remains constant.

If a charge is moved against the Coulomb force of an electric field, then:

The distance between the plates of a capacitor is $1 \ mm$. An electric field of $5 \times 10^5 \ V/m$ is produced between the two plates. What will be the change in the potential energy $(PE)$ of an electron if it is moved from one plate to the other?