$A$ 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 $\%$)?

Two charges $\pm 10\; \mu C$ are placed $5.0\; mm$ apart. Determine the electric field at $(a)$ a point $P$ on the axis of the dipole $15\; cm$ away from its centre $O$ on the side of the positive charge,as shown in Figure $(a),$ and $(b)$ a point $Q, 15\; cm$ away from $O$ on a line passing through $O$ and normal to the axis of the dipole,as shown in Figure.

The force on a charge situated on the axis of a dipole is $F$. If the charge is shifted to double the distance,the new force will be

An electric dipole is kept in a non-uniform electric field. It generally experiences:

$A$ positive charge $Q$ is distributed uniformly over a circular ring of radius $R$. $A$ point particle having a mass $m$ and a negative charge $-q$ is placed on its axis at a distance $x$ from the centre. Assuming $x \ll R$,find the time period of oscillation of the particle,if it is released from there [neglect gravity].

Consider a positively charged infinite cylinder with uniform volume charge density. An electric dipole consisting of $+Q$ and $-Q$ charges attached to opposite ends of a massless rod is oriented as shown in the figure. At the instant as shown in the figure, the dipole will experience,