The electric field due to a short electric dipole at a distance $r$ on the axial line from its mid-point is $x$ times the electric field at a distance $2r$ on the equatorial line from the mid-point of the dipole. Then,the value of $x$ is

$A$ given charge is situated at a certain distance from an electric dipole in the axial position and experiences a force $F$. If the distance of the charge is doubled,the force acting on the charge will be:

Two point charges $-4 \mu C$ and $4 \mu C$,constituting an electric dipole,are placed at $(-9, 0, 0) \ cm$ and $(9, 0, 0) \ cm$ in a uniform electric field of strength $10^4 \ NC^{-1}$. The work done on the dipole in rotating it from the equilibrium position through $180^{\circ}$ is: (in $mJ$)

An electric dipole is placed at an angle of $30^\circ$ with an electric field intensity of $2 \times 10^5 \, \text{NC}^{-1}$. It experiences a torque equal to $4 \, \text{Nm}$. The charge on the dipole,if the dipole length is $2 \, \text{cm}$,is:

The electric field intensity at a point on the axis of an electric dipole in air is $4 \text{ NC}^{-1}$. Then the electric field intensity at a point on the equatorial line which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant $4$ is

An electric dipole with dipole moment $p$ is placed with its axis at $30^{\circ}$ to a uniform electric field. The work done in rotating the dipole to a position where its axis is perpendicular to the field is