An electric dipole of mass $m$,charge $q$,and length $l$ is placed in a uniform electric field $\vec{E} = E_0 \hat{i}$. When the dipole is rotated slightly from its equilibrium position and released,the time period of its oscillations will be:

An electric dipole of moment $\vec{P}$ is placed in a uniform electric field $\vec{E}$ such that $\vec{P}$ points along $\vec{E}$. If the dipole is slightly rotated about an axis perpendicular to the plane containing $\vec{E}$ and $\vec{P}$ and passing through the centre of the dipole, the dipole executes simple harmonic motion. Consider $I$ to be the moment of inertia of the dipole about the axis of rotation. What is the time period of such oscillation?

Two charges $+q$ and $-q$ are kept at a certain distance apart. Then, at any point on the perpendicular bisector of the line joining the two charges:

$A$ molecule with a dipole moment $p$ is placed in an electric field of strength $E$. Initially,the dipole is aligned parallel to the field. If the dipole is to be rotated to be anti-parallel to the field,the work required to be done by an external agent is:

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of an $x-y$ coordinate system. Then:

Mention the direction of the electric dipole moment. Write the $SI$ unit of the electric dipole moment.