$A$ molecule of a substance has a permanent electric dipole moment of magnitude $10^{-29} \text{ C m}$. $2 \text{ mole}$ of this substance is polarized (at low temperature) by applying a strong electrostatic field of magnitude $10^6 \text{ V m}^{-1}$. What is the potential energy of the system? ($1 \text{ mole}$ of substance contains $6 \times 10^{23}$ molecules.)

Write the formulas for the electric field due to an electric dipole and the magnetic field due to a current-carrying loop at a point on their respective equatorial (bisector) lines at a distance $x$.

An electric dipole is formed by placing a charge of $4 \times 10^{-8} \ C$ at a distance of $2 \times 10^{-2} \ cm$. If it is placed in an electric field of $4 \times 10^8 \ N/C$,what is the maximum torque acting on it and the work done to rotate the dipole by $180^{\circ}$?

Three charges $q, -2q$ and $q$ are placed at $(x=0, y=a, z=0)$,$(x=0, y=0, z=0)$ and $(x=a, y=0, z=0)$ respectively. What is the resultant electric dipole moment?

Two identical electric point dipoles have dipole moments $\overrightarrow{p}_{1} = p\hat{i}$ and $\overrightarrow{p}_{2} = -p\hat{i}$ and are held on the $x$-axis at a distance $'a'$ from each other. When released,they move along the $x$-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is $'m'$,their speed when they are infinitely far apart is

$A$ point particle of charge $Q$ is located at $P$ along the axis of an electric dipole $1$ at a distance $r$ as shown in the figure. The point $P$ is also on the equatorial plane of a second electric dipole $2$ at a distance $r$. The dipoles are made of opposite charges $q$ separated by a distance $2a$. For the charged particle at $P$ not to experience any net force,which of the following correctly describes the situation?