$A$ dipole is placed in an electric field as shown. In which direction will it move?

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

If the electric field at a distance $x$ on the axis of an electric dipole is equal to the electric field at a distance $y$ on its equatorial line,what is the ratio $x : y$?

The potential at a point $P$ due to an electric dipole is $1.8 \times 10^5 \, V$. If $P$ is at a distance of $50 \, cm$ from the centre $O$ of the dipole and the line $OP$ makes an angle of $60^{\circ}$ with the positive side of the axial line of the dipole,what is the dipole moment?

Two charges $+q$ and $-q$ are placed at a distance $a$ in a uniform electric field. The dipole moment of the combination is $2qa(\cos \theta \hat{i} + \sin \theta \hat{j})$, where $\theta$ is the angle between the direction of the field and the line joining the two charges. Which of the following statement$(s)$ is/are correct?

Two electric dipoles of moment $P$ and $8P$ are placed in opposite directions on a line at a distance of $24 \text{ cm}$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $P$ is $x_1$. When $8P$ is replaced by $27P$ keeping all other quantities the same, the distance $x_1$ becomes $x_2$. The difference $|x_2 - x_1|$ is (All distances are measured from the centers of the dipoles.) (in $\text{ cm}$)