Three point charges $+q$, $+2q$, and $+Q$ are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of $Q$ in terms of $q$ is

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

Write an equation of electric potential at a point due to an electric dipole.

Two equal charges $q$ of opposite sign separated by a distance $2a$ constitute an electric dipole of dipole moment $p$. If $P$ is a point at a distance $r$ from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $\theta$ with the axis of the dipole,then the potential at $P$ is given by $(r \gg 2a)$ (where $p = 2qa$).

Derive the expression for the potential energy of an electric dipole in a uniform electric field.

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 $Q: q$ ?