An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is $p$ and moment of inertia is $I$. If the dipole is displaced slightly from the equilibrium position,then the angular frequency of its oscillations is

An electric dipole is placed in a uniform electric field $\vec{E}$ of magnitude $40\ N/C$. The graph shows the magnitude of the torque $\tau$ on the dipole versus the angle $\theta$ between the field $\vec{E}$ and the dipole moment $\vec{p}$. The magnitude of the dipole moment $\vec{p}$ is equal to:

An electric dipole is placed at the origin in the direction of the $x$-axis. $A$ point $P$ is at a distance of $20 \, cm$ from the origin $O$ such that $OP$ makes an angle of $\pi/3$ with the $x$-axis. If the electric field at point $P$ makes an angle $\theta$ with the $x$-axis,then the value of $\theta$ is:

When is the torque on an electric dipole in an electric field maximum?

An electric dipole with dipole moment $\vec{p} = \frac{p_0}{\sqrt{2}}(\hat{i}+\hat{j})$ is held fixed at the origin $O$ in the presence of a uniform electric field $\vec{E} = E_0 \hat{i}$. If the potential is constant on a circle of radius $R$ centered at the origin as shown in the figure,then the correct statement$(s)$ is/are:
($\varepsilon_0$ is the permittivity of free space,$R \gg$ dipole size)
$(1)$ $R = \left(\frac{p_0}{4 \pi \varepsilon_0 E_0}\right)^{1/3}$
$(2)$ The magnitude of the total electric field on any two points of the circle will be the same.
$(3)$ The total electric field at point $A$ is $\vec{E}_A = \sqrt{2} E_0(\hat{i}+\hat{j})$
$(4)$ The total electric field at point $B$ is $\vec{E}_B = 0$

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