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 $r \gg 2a$)

An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^5\,N C^{-1}$. It experiences a torque equal to $4\,N m$. Calculate the magnitude of charge on the dipole,if the dipole length is $2\,cm$. (in $,mC$)

An electric dipole with dipole moment $5 \times 10^{-6} \ Cm$ is aligned with the direction of a uniform electric field of magnitude $4 \times 10^5 \ N/C$. The dipole is then rotated through an angle of $60^{\circ}$ with respect to the electric field. The change in the potential energy of the dipole is (in $J$)

In the situation shown in the diagram,if $q \ll |Q|$ and $r \gg a$,find the net force on the free charge $-q$ and the net torque on it about $O$ at the instant shown. ($p = 2aQ$ is the dipole moment).

The electric field $\vec{E}$ at a point at a distance $r$ from the axis of a dipole is given by:

The electric field at point $A$ due to an electric dipole with dipole moment $p$ is perpendicular to the dipole moment vector $p$. The angle $\theta$ is: