An electric dipole is placed in a non-uniform electric field,then . . . . . . .

What is an electric dipole? What is an electric dipole moment?

Two electric dipoles of moment $P$ and $8P$ are placed in opposite directions on a line at a distance of $24 \text{ cm}$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $P$ is $x_1$. When $8P$ is replaced by $27P$ keeping all other quantities the same, the distance $x_1$ becomes $x_2$. The difference $|x_2 - x_1|$ is (All distances are measured from the centers of the dipoles.) (in $\text{ cm}$)

For the shown situation of two dipoles,determine the nature of the forces between them in cases $(I)$ and $(II)$.

$A$ point charge $q$ of mass $m$ is suspended vertically by a string of length $l$. $A$ point dipole of dipole moment $\overrightarrow{ p }$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole,the angles and distances is shown in the figure. If the work done in bringing the dipole to this position is $N \times (mgh)$,where $g$ is the acceleration due to gravity,then the value of $N$ is. . . . . . (Note that for three coplanar forces keeping a point mass in equilibrium,$\frac{F}{\sin \theta}$ is the same for all forces,where $F$ is any one of the forces and $\theta$ is the angle between the other two forces)

The electric field $\vec{E}$ at a point at a distance $r$ from the axis of a dipole is given by: