Two point charges $q_1 = 6 \mu C$ and $q_2 = 4 \mu C$ are kept at points $A$ and $B$ in air where $AB = 10 \ cm$. What is the increase in potential energy of the system when $q_2$ is moved towards $q_1$ by $2 \ cm$ (in $J$)?
$\left(\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}\right)$

Two charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively.
$(a)$ What is the electrostatic potential at the points $(0,0, z)$ and $(x, y, 0)$?
$(b)$ Obtain the dependence of potential on the distance $r$ of a point from the origin when $r/a > > 1$.
$(c)$ How much work is done in moving a small test charge from the point $(5,0,0)$ to $(-7,0,0)$ along the $x$-axis? Does the answer change if the path of the test charge between the same points is not along the $x$-axis?

When one electron is moved towards another electron,the electric potential energy of the system:

Write the $SI$ unit of electrostatic potential energy and its dimensional formula.

Derive the expression for the electric potential due to an electric dipole at a general point $P$ at a distance $r$ from its center.

Three point charges $3 \text{ nC}$,$6 \text{ nC}$,and $9 \text{ nC}$ are placed at the corners of an equilateral triangle of side $0.1 \text{ m}$. The potential energy of the system is: