The figure shows an electric field in which an electric dipole $\overrightarrow{P}$ is placed. Which of the following statements is correct?

An electric dipole is placed at a distance of $2 \ cm$ from an infinite plane sheet having positive charge density $\sigma_0$. Choose the correct option from the following.

$A$ 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.)

$A$ given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force $F$. If the distance of the charge is doubled,the force acting on the charge will be:

Two small spherical balls of mass $10 \ g$ each with charges $-2 \ \mu C$ and $2 \ \mu C$,are attached to two ends of a very light rigid rod of length $20 \ cm$. The arrangement is now placed near an infinite nonconducting charge sheet with a uniform charge density of $100 \ \mu C / m^2$ such that the length of the rod makes an angle of $30^{\circ}$ with the electric field generated by the charge sheet. The net torque acting on the rod is (Take $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2 / Nm^2$) (in $Nm$)

$A$ dipole having a dipole moment $p = 4 \, C-m$ is placed at the origin along the $x$-axis. $A$ point charge $q = 8 \, \mu C$ is fixed at $(4, 0, 0)$. Now,the dipole is rotated by an angle of $\frac{\pi}{2}$. Find the work done (in $mJ$) in rotating the dipole.