Two electric dipoles of moment $P$ and $27 P$ are placed on a line with their centres $24 \,cm$ apart. Their dipole moments are in opposite directions. At which point between the dipoles, measured from the centre of the dipole of moment $P$, will the electric field be zero (in $\,cm$)?

An electric dipole is placed in a uniform electric field $\vec{E}$ of magnitude $40\ N/C$. The graph shows the magnitude of the torque $\tau$ on the dipole versus the angle $\theta$ between the field $\vec{E}$ and the dipole moment $\vec{p}$. The magnitude of the dipole moment $\vec{p}$ is equal to:

An electric dipole is placed at an angle of $30^{\circ}$ in a non-uniform electric field. The electric dipole will experience:

An electric dipole with dipole moment $4 \times 10^{-9} \;C \,m$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^{4} \;N\,C ^{-1}$. Calculate the magnitude of the torque acting on the dipole.

$A$ 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:

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 $x = +r$	$(4) \ \vec{E}=\frac{p}{4 \pi \epsilon_0 r^3}(2\hat{i}-\hat{j})$
	$(5) \ \vec{E}=\frac{p}{\pi \epsilon_0 r^3} \hat{i}$