An electric dipole consisting of two opposite charges of $2 \times 10^{-6} \text{ C}$ separated by a distance of $3 \text{ cm}$ is placed in an electric field of $2 \times 10^5 \text{ N/C}$. The maximum torque acting on the dipole is:

$A$ dipole is placed in an electric field as shown. In which direction will it move?

Two parallel disks each having radius $R$ are separated by a distance $l$. The surface charge densities are $\sigma$ and $-\sigma$. The electric field at point $P$,a large distance $r$ along the axis of the disks 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 $x = +r$	$(4) \ \vec{E}=\frac{p}{4 \pi \epsilon_0 r^3}(2\hat{i}-\hat{j})$
	$(5) \ \vec{E}=\frac{p}{\pi \epsilon_0 r^3} \hat{i}$

Two identical electric point dipoles have dipole moments $\overrightarrow{p}_{1} = p\hat{i}$ and $\overrightarrow{p}_{2} = -p\hat{i}$ and are held on the $x$-axis at a distance $'a'$ from each other. When released,they move along the $x$-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is $'m'$,their speed when they are infinitely far apart is

An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^5\,N C^{-1}$. It experiences a torque equal to $4\,N m$. Calculate the magnitude of charge on the dipole,if the dipole length is $2\,cm$. (in $,mC$)