Two charges of $-4 \ \mu C$ and $+4 \ \mu C$ are placed at the points $A(1, 0, 4) \ m$ and $B(2, -1, 5) \ m$ located in an electric field $\vec{E} = 0.20 \ \hat{i} \ V/cm$. The magnitude of the torque acting on the dipole is $8 \sqrt{\alpha} \times 10^{-5} \ Nm$. Where $\alpha = $ . . . . . .

The force on a charge situated on the axis of a dipole is $F$. If the charge is shifted to double the distance,the new force will be

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

$A$ point $Q$ lies on the perpendicular bisector of an electric dipole with dipole moment $p$. If the distance of $Q$ from the dipole is $r$ (where $r$ is much larger than the size of the dipole),then the electric field at $Q$ is proportional to:

Two charges $\pm 10\; \mu C$ are placed $5.0\; mm$ apart. Determine the electric field at $(a)$ a point $P$ on the axis of the dipole $15\; cm$ away from its centre $O$ on the side of the positive charge,as shown in Figure $(a),$ and $(b)$ a point $Q, 15\; cm$ away from $O$ on a line passing through $O$ and normal to the axis of the dipole,as shown in Figure.

Point charges are fixed at the hour marks of a wall clock as shown. If the net dipole moment of the system is along the direction of the hour hand,then the time shown by the clock is: