Three charges $Q, (+q)$ and $(+q)$ are placed at the vertices of an equilateral triangle of side $l$ as shown in the figure. If the net electrostatic potential energy of the system is zero,then $Q$ is equal to

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

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

An electric dipole of dipole moment $\vec{p}$ is placed at the origin of the coordinate system along the $z$-axis. The amount of work required to move a charge $q$ from the point $A(a, 0, 0)$ to the point $B(0, 0, a)$ is,

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 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 $J$)?
$\left(\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}\right)$