Select the $WRONG$ statement about polar molecules.

Two charges $+q$ and $-q$ are placed at a distance $a$ in a uniform electric field. The dipole moment of the combination is $2qa(\cos \theta \hat{i} + \sin \theta \hat{j})$, where $\theta$ is the angle between the direction of the field and the line joining the two charges. Which of the following statement$(s)$ is/are correct?

An electric dipole of dipole moment $\vec{P}$ is placed in a uniform electric field $\vec{E}$. Which of the following statements are correct?
Statement $I$: The torque on the dipole is $\vec{\tau} = \vec{P} \times \vec{E}$
Statement $II$: The potential energy of the dipole is $U = -\vec{P} \cdot \vec{E}$
Statement $III$: The net force on the dipole is non-zero

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

Two opposite and equal charges $4 \times 10^{-8} \, C$ are placed $2 \times 10^{-2} \, cm$ apart,forming a dipole. If this dipole is placed in an external electric field of $4 \times 10^8 \, N/C$,what are the values of the maximum torque and the work done in rotating it through $180^\circ$?