An electric dipole of dipole moment $\vec{p}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole by $90^{\circ}$ is:

An electric dipole consisting of two opposite charges of $2 \times 10^{-6} \, C$ each,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:

As shown in the figure,a particle $A$ of mass $2m$ and carrying charge $q$ is connected by a light rigid rod of length $L$ to another particle $B$ of mass $m$ and carrying charge $-q$. The system is placed in an electric field $\vec E$. The electric force on a charge $q$ in an electric field $\vec E$ is $\vec F = q \vec E$. After the system settles into equilibrium,one particle is given a small push in the transverse direction so that the rod makes a small angle $\theta_0$ with the electric field. Find the maximum tension in the rod.

An electrical dipole coincides on the $z$-axis and its midpoint is at the origin of the coordinate system. The electric field at an axial point at a distance $z$ from the origin is $\vec{E}(z)$ and the electric field at an equatorial point at a distance $y$ from the origin is $\vec{E}(y)$. Here $z = y \gg a$,so $\left| \frac{\vec{E}(z)}{\vec{E}(y)} \right| = . . . . . . . .$.

An electric dipole is situated in an electric field as shown in the figure. The dipole and electric field are both in the plane of the paper. The dipole is rotated about an axis perpendicular to the paper at point $A$ in an anti-clockwise direction. If the angle of rotation is measured with respect to the direction of the electric field,then the torque for different values of the angle of rotation $\theta$ is correctly represented by which graph among $a, b, c, d$ given in the figure?

Two charges of $+25 \times 10^{-9} \, C$ and $-25 \times 10^{-9} \, C$ are placed $6 \, m$ apart. Find the ratio of the electric field intensity at a point $4 \, m$ from the center of the electric dipole on the $(i)$ axial line and $(ii)$ equatorial line.