An electric dipole formed by two particles fixed at the end of a light rod of length $l$. The mass of each particle is $m$ and the charges are $-q$ and $+q$.

The system is placed in such a way that the dipole axis is parallel to a uniform electric field $E$ that exists in the region. The dipole is slightly rotated about its centre and released. Show that for small angular displacement, the motion is angular SHM and evaluate its time period.

A dipole having dipole moment $p$ is placed at the axis of a charged ring having charge $Q$ and radius $R$, at a distance $x$ from the centre as shown in the figure. Find the force experienced by the dipole moment $\overrightarrow{p}=p\widehat{\mathrm{i}}$ placed along the axes of the uniformly charged ring.

An isolated charge $q_1$ of mass $m$ is suspended freely by a thread of length $l$. Another charge $q_2$ is brought near it $\left(r\gg l\right)$. When $q_1$ is in equilibrium, tension in thread will be

An electroscope is given a positive charge, causing its foil leaves to separate. When an object is brought near the top plate of the electroscope, the foils separate even further. We conclude

Which of the following four figures correctly show the forces that three charged particles exert on each other?
$\left(\mathrm{i}\right)$

$\left(\mathrm{ii}\right)$
$\left(\mathrm{iii}\right)$

$\left(\mathrm{iv}\right)$

Three charged particles are placed on a straight line as shown in the figure. $q_1$ and $q_2$ are fixed, but $q_3$ can be moved. Under the action of the forces from $q_1$ and $q_2$, $q_3$ is in equilibrium. What is the relation between $q_1$ and $q_2$?