Give definition of electric dipole moment.

Figure shows a charged rod, bent in the form of an arc of a circle. The charge distribution on the rod is shown in figure. The assembly is kept in a uniform electric field.

(a) Find the dipole moment of the rod.

(b) For small angular displacement of the system, find the time period of oscillation of the system.

When is an electric dipole in a stable equilibrium in a uniform electric field.

Three charges $+2q, -q$ are $\mathit{-}q$  are placed at the vertices $A, B$ and $C$ respectively of an equilateral triangle $ABC$ of side $a$. Find the magnitude of dipole moment of this system.

Demonstrate that the potential of the field generated by a dipole, with electric moment $\overrightarrow{\mathit{P}}$, may be represented as $\mathrm{\phi }=\frac{\overrightarrow{p}·\overrightarrow{r}}{4\mathrm{\pi }{\epsilon }_0{r}^3}$, where $\overrightarrow{\mathit{r}}$ is the radius vector. Using this expression, find the magnitude of the electric field strength vector as a function of $r$ and $\mathrm{\theta }$.