The electric potential at a point on the axis of an electric dipole depends on the distance $r$ of the point from the dipole as

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 $Q: q$ ?

Three charges $Q, +q$ and $+q$ are placed at the vertices of a right-angled isosceles triangle as shown in the figure. If the net electrostatic potential energy of the system is zero,the value of $Q$ is

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

When two electrons $(e^-)$ move towards each other,the electrostatic potential energy of the system will:

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?