$4$ charges are placed each at a distance $a$ from the origin. The dipole moment of the configuration is

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.