$A$ point $Q$ lies on the perpendicular bisector of an electric dipole with dipole moment $p$. If the distance of $Q$ from the dipole is $r$ (where $r$ is much larger than the size of the dipole),then the electric field at $Q$ is proportional to:

Three point charges $q, -2q$ and $q$ are placed along the $x$-axis at $x = -a, 0$ and $a$ respectively. As $a \rightarrow 0$ and $q \rightarrow \infty$ while $qa^2 = Q$ remains finite, the electric field at a point $P$, at a distance $x$ $(x \gg a)$ from $x = 0$ is $E = \frac{\alpha Q}{4 \pi \epsilon_0 x^\beta} \hat{i}$. Then:

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:

An electric dipole with dipole moment $5 \times 10^{-6} \ Cm$ is aligned with the direction of a uniform electric field of magnitude $4 \times 10^5 \ N/C$. The dipole is then rotated through an angle of $60^{\circ}$ with respect to the electric field. The change in the potential energy of the dipole is (in $J$)

An electric dipole consists of two equal and opposite charges of $2 \ \mu C$ separated by a distance of $3 \ cm$. If it is placed in an external electric field of $2 \times 10^{5} \ N/C$,the maximum torque experienced by it is:

$A$ 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 $\%$)?