What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line (in $^o$)?

$A$ dipole with an electric moment $\vec{p}$ is located at a distance $r$ from a long thread charged uniformly with a linear charge density $\lambda$. Find the force $F$ acting on the dipole if the vector $\vec{p}$ is oriented along the thread.

One end of a spring of negligible unstretched length and spring constant $k$ is fixed at the origin $(0,0)$. $A$ point particle of mass $m$ carrying a positive charge $q$ is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole $\overrightarrow{p}$ pointing towards the charge $q$ is fixed at the origin,the spring gets stretched to a length $\ell$ and attains a new equilibrium position. If the point mass is now displaced slightly by $\Delta \ell \ll \ell$ from its equilibrium position and released,it is found to oscillate at frequency $\frac{1}{\delta} \sqrt{\frac{k}{m}}$. The value of $\delta$ is. . . . . .

An electric field of $1000\,V/m$ is applied to an electric dipole at an angle of $45^\circ$. The value of the electric dipole moment is $10^{-29}\,C\cdot m$. What is the potential energy of the electric dipole?

Two electric dipoles of moments $p$ and $27 p$ are placed in opposite directions on a line at a distance of $24 \,cm$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $p$ is

An electric dipole with dipole moment $P$ and moment of inertia $I$ is placed in a uniform electric field of intensity $E$. If the dipole is slightly rotated,the angular frequency of its oscillation is ........