Three point charges $q, -2q$ and $q$ are placed along the $x$-axis at $x = -a, 0$ and $a$ respectively. As $a \rightarrow 0$ and $q \rightarrow \infty$ while $qa^2 = Q$ remains finite,the electric field at a point $P$,at a distance $x$ $(x \gg a)$ from $x = 0$ is $E = \frac{\alpha Q}{4 \pi \epsilon_0 x^\beta} \hat{i}$. Then:

$A$ 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:

If $E_{a}$ and $E_{q}$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance $r$ from the centre of the dipole,then

Give the definition of electric dipole moment using the equation of torque.

$A$ 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?

Point charges are fixed at the hour marks of a wall clock as shown. If the net dipole moment of the system is along the direction of the hour hand,then the time shown by the clock is: