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 $60^\circ$.

$A$ rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_1 = E_0\hat{i}$. If another electric field $\vec{E}_2 = 2E_0(\hat{j} + \hat{k})$ is introduced to the system,what will be the percentage change in the frequency of the oscillation (approximate) (in $\%$)?

$A$ dipole is placed in a uniform electric field,its potential energy will be minimum when the angle between its axis and field is

For an electric dipole, if the magnitude of each charge is $10^{-10} \, \text{stC}$ and the distance between them is $1 \, \mathring{A}$, then the dipole moment is:

Two point dipoles $p \hat{k}$ and $\frac{p}{2} \hat{k}$ are located at $(0, 0, 0)$ and $(1 \text{ m}, 0, 2 \text{ m})$ respectively. The resultant electric field due to the two dipoles at the point $(1 \text{ m}, 0, 0)$ 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 $r = 10R$.