The electric field due to a dipole at a distance $r$ on its axis is

An electric dipole is placed in a non-uniform electric field,then . . . . . . .

An electric dipole consists of two particles, each of mass $1 \ kg$, separated by $1 \ m$, carrying charges $1 \ \mu C$ and $-1 \ \mu C$ respectively. It is in equilibrium in a uniform electric field of $2 \times 10^4 \ Vm^{-1}$. If it is deflected by a small angle $2^{\circ}$, the minimum time taken by it to come back again to the mean position is (in seconds): (in $\pi$)

An electric dipole of moment $p$ is placed in an electric field of intensity $E$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole is zero when $\theta = 90^o$,the torque and the potential energy of the dipole will respectively be

An electric dipole is placed at the origin in the direction of the $x$-axis. $A$ point $P$ is at a distance of $20 \, cm$ from the origin $O$ such that $OP$ makes an angle of $\pi/3$ with the $x$-axis. If the electric field at point $P$ makes an angle $\theta$ with the $x$-axis,then the value of $\theta$ is:

An electric dipole having each charge of magnitude $2 \mu C$ is placed in an electric field of intensity $8 \times 10^{4} \ N/C$. If the maximum torque acting on the dipole is $4 \times 10^{-3} \ N \cdot m$,the length of the dipole is: (in $mm$)