The electric field $\vec{E}$ at a point at a distance $r$ from the axis of a dipole is given by:

The figure shows electric field lines in which an electric dipole $p$ is placed as shown. Which of the following statements is correct?

Obtain the equation for the electric field produced by an electric dipole at a point on its equatorial plane.

An electric dipole consists of two particles, each of mass $1 \ kg$, separated by $1 \ m$, carrying charges $1 \ \mu C$ and $-1 \ \mu C$ respectively. It is in equilibrium in a uniform electric field of $2 \times 10^4 \ Vm^{-1}$. If it is deflected by a small angle $2^{\circ}$, the minimum time taken by it to come back again to the mean position is (in seconds): (in $\pi$)

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 $180^{\circ}$?

Match Column-$I$ with Column-$II$ related to an electric dipole of dipole moment $\vec{p}$ that is placed in a uniform electric field $\overrightarrow{E}$.

Column-$I$ (Angle between $\vec{p}$ and $\vec{E}$)	Column-$II$ (Potential energy of the dipole)
$a. 180^{\circ}$	$i. -pE$
$b. 120^{\circ}$	$ii. pE$
$c. 90^{\circ}$	$iii. \frac{1}{2} pE$
	$iv. 0$