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

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

Two charges $10 \mathrm{\mu C}$ and $-10 \mathrm{\mu C}$ are placed at points A and B separated by a distance of $10 \mathrm{cm}$. Find the electric field at a point P on the perpendicular bisector of AB, at a distance of $12 \mathrm{cm}$ from its mid-point.

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

Two ideal electric dipoles $A$ and $B$, having their dipole moment $p_1$ and $p_2$ respectively are placed on a plane with their centres at $O$ as shown in the figure. At point $C$ on the axis of dipole $A$, the resultant electric field is making an angle of $37°$ with the axis. The ratio of the dipole moment of $A$ and $B,\frac{p_1}{p_2}$ is$:($ take $\left.\sin 37°=\frac{3}{5}\right)$

In the figure the net torque acting on the dipole is

An electric dipole having point charges $+q$ and $-q$, separated by a fixed distance $d$ is kept under the influence of a uniform electric field $E$, such that the axis of the dipole is making an angle $\theta =45°$ with the direction of $E$, as shown in the figure. If the electric dipole is allowed to rotate in the $xy$-plane with its center being stationary, what is the magnitude of the net torque acting on the electric dipole?