Three charges $-q, Q$ and $-q$ are placed respectively at equal distances on a straight line. If the potential energy of the system of three charges is zero,then what is the ratio of $Q: q$ ?

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

The electric potential at a distance of $3 \, m$ on the axis of a short dipole of dipole moment $4 \times 10^{-12} \, C \cdot m$ is ......... $mV$.

Three particles,each having a charge of $10 \mu C$,are placed at the corners of an equilateral triangle of side $10 \ cm$. The electrostatic potential energy of the system is (Given $\frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \ N \cdot m^{2}/C^{2}$):

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?

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