At the midpoint of the axis of an electric dipole,which of the following is true?

An electric dipole is placed along the $x$-axis with its center at the origin. The line $OP$ makes an angle of $\frac{\pi}{3}$ with the $x$-axis. If the electric field at point $P$ makes an angle $\theta$ with the $x$-axis,then $\theta$ is equal to:

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(+d, 0)$ respectively of an $(x, y)$ coordinate system. Then:

An electric dipole is formed by two equal and opposite charges $q$ with separation $d$. The charges have the same mass $m$. It is kept in a uniform electric field $E$. If it is slightly rotated from its equilibrium orientation,then its angular frequency $\omega$ is

The potential at a point due to an electric dipole will be maximum and minimum when the angles between the axis of the dipole and the line joining the point to the dipole are respectively:

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?