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 $mm$)

$A$ dipole comprises two charged particles of identical magnitude $q$ and opposite in nature. The mass $m$ of the positive charged particle is half of the mass of the negative charged particle $(2m)$. The two charges are separated by a distance $l$. If the dipole is placed in a uniform electric field $E$ such that the dipole axis makes a very small angle $\theta$ with the electric field $E$,the angular frequency of the oscillations of the dipole when released is given by:

Two short electric dipoles are placed as shown. The energy of electric interaction between these dipoles will be

An electric dipole with dipole moment $4 \times 10^{-9} \text{ Cm}$ is aligned at $60^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^4 \text{ NC}^{-1}$. Calculate the magnitude of the torque acting on the dipole.

Two short dipoles $A$ and $B$, $A$ having charges $\pm 2 \mu C$ and length $1 \text{ cm}$, and $B$ having charges $\pm 4 \mu C$ and length $1 \text{ cm}$, are placed with their centres $80 \text{ cm}$ apart as shown in the figure. The electric field at a point $P$, equidistant from the centres of both dipoles, is . . . . . . $\text{N/C}$.

An electric dipole is placed at an angle of $30^o$ to a non-uniform electric field. The dipole will experience: