The electric field due to a short electric dipole at a large distance $(r)$ from the center of the dipole on the equatorial plane varies with distance as:

At any point on the perpendicular bisector of the line joining two equal and opposite charges,which of the following is true?

If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$,then the torque acting on it is given by:

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

Three charges are arranged on the vertices of a right-angled triangle as shown in the figure. The magnitude of the dipole moment of the combination in the unit of $C-cm$ is:

List-$I$ shows four configurations,each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude $p$,oriented as marked by arrows in the figures. In all the configurations,the dipoles are fixed such that they are at a distance $2r$ apart along the $x$-direction. The midpoint of the line joining the two dipoles is $X$. The possible resultant electric fields $\vec{E}$ at $X$ are given in List-$II$. Choose the option that describes the correct match between the entries in List-$I$ to those in List-$II$.

List-$I$	List-$II$
$(P)$ Two dipoles pointing in $+\hat{j}$ direction at $x = -r$ and $x = +r$	$(1) \ \vec{E}=0$
$(Q)$ Two dipoles pointing in $+\hat{j}$ and $-\hat{j}$ direction at $x = -r$ and $x = +r$ respectively	$(2) \ \vec{E}=-\frac{p}{2 \pi \epsilon_0 r^3} \hat{j}$
$(R)$ Two dipoles pointing in $+\hat{j}$ and $+\hat{i}$ direction at $x = -r$ and $x = +r$ respectively	$(3) \ \vec{E}=-\frac{p}{4 \pi \epsilon_0 r^3}(\hat{i}-\hat{j})$
$(S)$ Two dipoles pointing in $+\hat{i}$ direction at $x = -r$ and $x = +r$	$(4) \ \vec{E}=\frac{p}{4 \pi \epsilon_0 r^3}(2\hat{i}-\hat{j})$
	$(5) \ \vec{E}=\frac{p}{\pi \epsilon_0 r^3} \hat{i}$