An electric dipole consisting of two opposite charges of $2 \times 10^{-6} \ C$ separated by a distance of $3 \ cm$ is placed in an electric field of $2 \times 10^5 \ N/C$. The maximum torque on the dipole will be

Torque acting on an electric dipole in a uniform electric field is maximum when the angle between $\vec{p}$ and $\vec{E}$ is . . . . . . . (in $^{\circ}$)

$A$ dipole is placed in an electric field as shown. In which direction will it move?

$A$ 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 $\%$)?

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:

$A$ given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force $F$. If the distance of the charge is doubled,the force acting on the charge will be: