Determine the electric dipole moment of the system of three charges,placed on the vertices of an equilateral triangle,as shown in the figure.

Two electric dipoles of dipole moments $1.2 \times 10^{-30} \, C \cdot m$ and $2.4 \times 10^{-30} \, C \cdot m$ are placed in two different uniform electric fields of strengths $5 \times 10^{4} \, N \cdot C^{-1}$ and $15 \times 10^{4} \, N \cdot C^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of $x$ is $.....$

Two charges $10 \mu C$ and $-10 \mu C$ are placed at points $A$ and $B$ separated by a distance of $10 \ cm$. Find the electric field at a point $P$ on the perpendicular bisector of $AB$,at a distance of $12 \ cm$ from its midpoint.

An electric dipole has a charge of magnitude $q$ and a dipole moment $p$. It is placed in a uniform electric field $E$. If its dipole moment is aligned with the direction of the electric field, the force acting on it and its potential energy will be, respectively:

An electric dipole is formed by two equal and opposite charges $q$ with separation $d$. The charges have the same mass $m$. It is kept in a uniform electric field $E$. If it is slightly rotated from its equilibrium orientation,then its angular frequency $\omega$ is

An electric dipole is placed on the $x$-axis with its center at the origin. The line $OP$ makes an angle $\theta$ with the $x$-axis. If the electric field at point $P$ is in the direction of the $y$-axis,what is the value of $\theta$?