Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point $O$ and perpendicular to the plane of the figure at a distance of $x (>> a)$ from $O$ is

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 $\,cm$)?

Two point charges $-4 \mu C$ and $4 \mu C$,constituting an electric dipole,are placed at $(-9, 0, 0) \ cm$ and $(9, 0, 0) \ cm$ in a uniform electric field of strength $10^4 \ NC^{-1}$. The work done on the dipole in rotating it from the equilibrium position through $180^{\circ}$ is: (in $mJ$)

Electric charges $q, q, -2q$ are placed at the corners of an equilateral triangle $ABC$ of side $l$. The magnitude of the electric dipole moment of the system is

Two ideal electric dipoles $A$ and $B$ having dipole moments $p_{1}$ and $p_{2}$ respectively are placed on a plane with their centers at $O$ as shown in the figure. At point $C$ on the axis of dipole $A$,the resultant electric field makes an angle of $37^{\circ}$ with the axis. The ratio of the dipole moments of $A$ and $B$,$\frac{p_{1}}{p_{2}}$ is $....$ (take $\sin 37^{\circ}=\frac{3}{5}$)

At the midpoint of the axis of an electric dipole,which of the following is true?