What is the force acting on an electric dipole in a uniform electric field?

An electric dipole of moment $\vec{p}$ is kept in a uniform electric field $\vec{E}$. The angle between $\vec{p}$ and $\vec{E}$ is $30^\circ$. Calculate the work done by the field when the angle is increased to $60^\circ$.

The electric field due to an electric dipole at a distance $r$ from its centre in the axial position is $E$. If the dipole is rotated through an angle of $90^{\circ}$ about its perpendicular axis,the electric field at the same point will be

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

An electric dipole has the magnitude of its charge as $q$ and its dipole moment is $p$. It is placed in a uniform electric field $E$. If its dipole moment is along the direction of the field,the force on it and its potential energy are respectively

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