The potential energy of a system of two equal negative point charges of $2 \mu C$ each,held $1 \ m$ apart in air,is . . . . . . . $\left( k = 9 \times 10^9 \text{ SI units} \right)$

Two particles of charges $4 \text{ nC}$ and $Q$ are kept in air with a separation of $10 \text{ cm}$ between them. If the electrostatic potential energy of the system is $1.8 \mu \text{ J}$, then $Q$ is: (in $\text{ nC}$)

The electrostatic potential due to an electric dipole at a distance '$r$' varies as:

Write an equation for the electric potential due to an electric dipole and state its important features. Discuss its special cases.

Write an equation of electric potential at a point on the axis of an electric dipole.

Two electric dipoles $A$ and $B$ with respective dipole moments $\overrightarrow {{d_A}} = - 4\,qa\,\hat i$ and $\overrightarrow {{d_B}} = 2\,qa\,\hat i$ are placed on the $x-$ axis with a separation $R$,as shown in the figure. The distance from $A$ at which both of them produce the same potential is