Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of an $x-y$ coordinate system. Then:

For a dipole with charge $q = 2 \times 10^{-6} \, C$ and separation $d = 0.01 \, m$,calculate the maximum torque acting on this dipole if it is placed in an electric field $E = 5 \times 10^5 \, N/C$.

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

Point $P$ lies on the axis of a dipole. If the dipole is rotated by $90^o$ anticlockwise,the electric field vector $\vec{E}$ at $P$ will rotate by

An electric dipole is placed at an angle $60^{\circ}$ with an electric field of strength $4 \times 10^5 \,N/C$. It experiences a torque equal to $8 \sqrt{3} \,Nm$. Calculate the charge on the dipole,if the dipole length is $4 \,cm$.

An electric dipole in a uniform electric field experiences (when it is placed at an angle $\theta$ with the field):