Three identical dipoles are arranged as shown below. What will be the net electric field at $P$ $\left( {k = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$?

$A$ neutral water molecule $(H_2O)$ in its vapor state has an electric dipole moment of magnitude $6.4 \times 10^{-30} \ C \cdot m$. How far apart are the molecule's centers of positive and negative charge?

$A$ 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:

An electric dipole is placed in a non-uniform electric field such that the angle between $\vec{p}$ and $\vec{E}$ is not $0^{\circ}$ or $180^{\circ}$. It experiences . . . . . . .

Intensity of an electric field $E$ due to a dipole,depends on distance $r$ as

Two charges of $-4 \ \mu C$ and $+4 \ \mu C$ are placed at the points $A(1, 0, 4) \ m$ and $B(2, -1, 5) \ m$ located in an electric field $\vec{E} = 0.20 \ \hat{i} \ V/cm$. The magnitude of the torque acting on the dipole is $8 \sqrt{\alpha} \times 10^{-5} \ Nm$. Where $\alpha = $ . . . . . .