$A$ 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 $\%$)?

An electric dipole of dipole moment $P$ is placed parallel to a uniform electric field of intensity $E$. On rotating it through an angle of $90^\circ$ from this position,the amount of work done is . . . . . . .

An electric dipole is placed at an angle $60^{\circ}$ with an electric field of strength $4 \times 10^5 \,N/C$. It experiences a torque equal to $8 \sqrt{3} \,Nm$. Calculate the charge on the dipole,if the dipole length is $4 \,cm$.

The potential at a point $P$ due to an electric dipole is $1.8 \times 10^5 \, V$. If $P$ is at a distance of $50 \, cm$ from the centre $O$ of the dipole and the line $OP$ makes an angle of $60^{\circ}$ with the positive side of the axial line of the dipole,what is the dipole moment?

$A$ point particle of charge $Q$ is located at $P$ along the axis of an electric dipole $1$ at a distance $r$ as shown in the figure. The point $P$ is also on the equatorial plane of a second electric dipole $2$ at a distance $r$. The dipoles are made of opposite charges $q$ separated by a distance $2a$. For the charged particle at $P$ not to experience any net force,which of the following correctly describes the situation?

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: