The electric field intensity at a point on the axis of an electric dipole in air is $4 \text{ NC}^{-1}$. Then the electric field intensity at a point on the equatorial line which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant $4$ is

An electric dipole is placed along the $x$-axis at the origin $O$. $A$ point $P$ is at a distance of $20 \, cm$ from this origin such that $OP$ makes an angle $\frac{\pi}{3}$ with the $x$-axis. If the electric field at $P$ makes an angle $\theta$ with the $x$-axis,the value of $\theta$ would be

$A$ 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?

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)
$a. 180^{\circ}$	$i. -pE$
$b. 120^{\circ}$	$ii. pE$
$c. 90^{\circ}$	$iii. \frac{1}{2} pE$
	$iv. 0$

In the situation shown in the diagram,if $q \ll |Q|$ and $r \gg a$,find the net force on the free charge $-q$ and the net torque on it about $O$ at the instant shown. ($p = 2aQ$ is the dipole moment).

At the midpoint of the axis of an electric dipole,which of the following is true?