For a system of two dipoles ${\overrightarrow{P}}_1$ and ${\overrightarrow{P}}_2$ as shown in the figure (both are at origin and perpendicular to each other along $x$ and $y$-axes, respectively) $(P_1$ and $P_2$) denotes magnitude of ${\overrightarrow{P}}_1$ and ${\overrightarrow{P}}_2$ is quite large in comparison to dimensions of dipoles, $\overrightarrow{E}$ is resultant electric field and $QPR$ is a quarter of circle whose centre is at $O$).

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 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 $\left.\sin 37°=\frac{3}{5}\right)$

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.

Derive an expression for electric field intensity due to an electric dipole at a point on its axial line.

5 marks

Define electric dipole moment. Give its unit.

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

The magnitude of electric intensity at a distance $\text{'}\mathrm{r}\text{'}$ from the centre of an electric dipole along its axial line is $\mathrm{E}$. The distance of the point from the centre of the electric dipole along its equatorial line at which the electric intensity has the same value $\mathrm{E}$ is:

Derive an expression for electric field intensity due to an electric dipole at a point on its axial line.