The relation between the intensity of the electric field of an electric dipole at a distance $r$ from its centre on its axis and the distance $r$ is . . . . . . . (where $r \gg 2a$)

$A$ dipole with dipole moment $p$ and moment of inertia $I$ is placed in a uniform electric field $E$. If it is displaced slightly from its stable equilibrium position,the period of oscillation of the dipole is

If the magnitude of the intensity of the electric field at a distance $x$ on the axial line and at a distance $y$ on the equatorial line for a given electric dipole are equal,then the ratio $x:y$ is:

$A$ 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 $:$

In a certain region of space,the electric field is along the $z$-direction throughout. The magnitude of the electric field is,however,not constant but increases uniformly along the positive $z$-direction at the rate of $10^{5} \; N \, C^{-1}$ per meter. What are the force and torque experienced by a system having a total dipole moment equal to $10^{-7} \; C \, m$ in the negative $z$-direction?

Three point charges of $+2q, +2q$ and $-4q$ are placed at the corners $A, B$ and $C$ of an equilateral triangle $ABC$ of side '$x$'. The magnitude of the electric dipole moment of this system is