Two tiny electric dipoles of dipole moments $P_1$ and $P_2$ are placed at a distance $r$ coaxially. Find the magnitude of the electrostatic force between them.

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 $\text{ cm}$)

An electric dipole is placed at the origin in the direction of the $x$-axis. $A$ point $P$ is at a distance of $20 \, cm$ from the origin $O$ such that $OP$ makes an angle of $\pi/3$ with the $x$-axis. If the electric field at point $P$ makes an angle $\theta$ with the $x$-axis,then the value of $\theta$ is:

An electric dipole consisting of two opposite charges of $2 \times 10^{-6} \ C$ separated by a distance of $3 \ cm$ is placed in an electric field of $2 \times 10^5 \ N/C$. The maximum torque on the dipole will be

Obtain the expression for the torque acting on an electric dipole in a uniform external electric field.

An electric field of $1000\,V/m$ is applied to an electric dipole at an angle of $45^\circ$. The value of the electric dipole moment is $10^{-29}\,C\cdot m$. What is the potential energy of the electric dipole?