What is the net charge on an electric dipole? Why?

An electric dipole of length $4 \ cm$ is placed with its axis making an angle of $60^{\circ}$ with a uniform electric field. It experiences a torque of $4 \sqrt{3} \ Nm$. Calculate the magnitude of the electric field. (The dipole has charges $\pm 8 \ nC$)

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 dipole is kept on the axis of a uniformly charged ring at a distance of $R/\sqrt{2}$ from the center of the ring. The direction of the dipole moment is along the axis. The dipole moment is $P$,the charge of the ring is $Q$,and the radius of the ring is $R$. The force on the dipole is nearly:

An electric dipole is placed on the $x$-axis with its center at the origin. The line $OP$ makes an angle $\theta$ with the $x$-axis. If the electric field at point $P$ is in the direction of the $y$-axis,what is the value of $\theta$?

An electric dipole having dipole moment $P = q \times 2\ell$ is placed in a uniform electric field $E$. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively