An electric dipole with dipole moment $P$ and moment of inertia $I$ is placed in a uniform electric field of intensity $E$. If the dipole is slightly rotated,the angular frequency of its oscillation is ........

Two opposite and equal charges $4 \times 10^{-8} \, C$ are placed $2 \times 10^{-2} \, cm$ apart,forming a dipole. If this dipole is placed in an external electric field of $4 \times 10^8 \, N/C$,what are the values of the maximum torque and the work done in rotating it through $180^\circ$?

If the electric field intensity at a distance $x$ on the axis of a dipole is equal to the electric field intensity at a distance $y$ on its equatorial line,then the ratio $x:y$ is:

Three identical small electric dipoles are arranged parallel to each other at equal separation $a$ as shown in the figure. Their total interaction energy is $U$. Now,one of the end dipoles is gradually reversed. How much work is done by the electric forces?

$A$ dipole with two electric charges of $2 \ \mu C$ magnitude each,with separation distance $0.5 \ \mu m$,is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of $5 \ V$ is applied. Separation between the plates is $0.5 \ mm$. If the dipole is rotated by $30^{\circ}$ from the axis,it tends to realign in the direction due to a torque. The value of torque is $:$

Point $P$ lies on the axis of a dipole. If the dipole is rotated by $90^o$ anticlockwise,the electric field vector $\vec{E}$ at $P$ will rotate by