$A$ molecule with a dipole moment $p$ is placed in an electric field of strength $E$. Initially,the dipole is aligned parallel to the field. If the dipole is to be rotated to be anti-parallel to the field,the work required to be done by an external agent is:

$A$ small electric dipole $\vec{p}_0$,having a moment of inertia $I$ about its center,is kept at a distance $r$ from the center of a spherical shell of radius $R$. The surface charge density $\sigma$ is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle $\theta$ as shown in the figure. While staying at a distance $r$,the dipole is free to rotate about its center. If released from rest,then which of the following statement$(s)$ is (are) correct? [$\varepsilon_0$ is the permittivity of free space.]
$(A)$ The dipole will undergo small oscillations at any finite value of $r$.
$(B)$ The dipole will undergo small oscillations at any finite value of $r > R$.
$(C)$ The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{\sigma p_0}{4 \varepsilon_0 I}}$ at $r = 2R$.
$(D)$ The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{\sigma p_0}{100 \varepsilon_0 I}}$ at $r = 10R$.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: If an electric dipole of dipole moment $30 \times 10^{-5} \, Cm$ is enclosed by a closed surface,the net flux coming out of the surface will be zero.
Reason $R$: An electric dipole consists of two equal and opposite charges.
In the light of the above statements,choose the correct answer from the options given below:

Two short electric dipoles $A$ and $B$ having dipole moments $p_1$ and $p_2$ respectively are placed with their axes mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ makes an angle of $60^{\circ}$ with the line joining points $O$ and $x$. The ratio of the dipole moments $p_2/p_1$ is . . . . . . .

Explain the force acting on an electric dipole when it is placed parallel or anti-parallel to a non-uniform electric field.

Two charges $+3.2 \times 10^{-19} \text{ C}$ and $-3.2 \times 10^{-19} \text{ C}$ placed at $2.4 \text{ Å}$ apart form an electric dipole. It is placed in a uniform electric field of intensity $4 \times 10^5 \text{ V/m}$. The electric dipole moment is