An electric dipole of moment $\overrightarrow{p}$ is placed normal to the lines of force of electric intensity $\overrightarrow{E}$. The work done in deflecting it through an angle of $180^\circ$ is:

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

Three charges $+2q$,$+3q$,and $-4q$ are situated at $(0, -3a)$,$(2a, 0)$,and $(-2a, 0)$ respectively in the $xy$ plane. The resultant dipole moment about the origin is . . . . . .

Two electric dipoles of moment $P$ and $64 P$ are placed in opposite directions on a line at a distance of $25 \ cm$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $P$ is.....$cm$.

There exists a non-uniform electric field along the $x-$ axis as shown in the figure below. The field increases at a uniform rate along the $+ve$ $x-$ axis. $A$ dipole is placed inside the field as shown. Which one of the following is correct for the dipole?

An electric dipole having dipole moment $P = q \times 2\ell$ is placed in a uniform electric field $E$. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively