Two point charges $-4 \mu C$ and $4 \mu C$,constituting an electric dipole,are placed at $(-9, 0, 0) \ cm$ and $(9, 0, 0) \ cm$ in a uniform electric field of strength $10^4 \ NC^{-1}$. The work done on the dipole in rotating it from the equilibrium position through $180^{\circ}$ is: (in $mJ$)

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.

The electric field at point $A$ due to an electric dipole with dipole moment $p$ is perpendicular to the dipole moment vector $p$. The angle $\theta$ is:

Four charges are placed at a distance $a$ from the origin as shown in the figure. The dipole moment of the configuration is:

One end of a spring of negligible unstretched length and spring constant $k$ is fixed at the origin $(0,0)$. $A$ point particle of mass $m$ carrying a positive charge $q$ is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole $\overrightarrow{p}$ pointing towards the charge $q$ is fixed at the origin,the spring gets stretched to a length $\ell$ and attains a new equilibrium position. If the point mass is now displaced slightly by $\Delta \ell \ll \ell$ from its equilibrium position and released,it is found to oscillate at frequency $\frac{1}{\delta} \sqrt{\frac{k}{m}}$. The value of $\delta$ is. . . . . .

Two charges each of magnitude $0.01\,C$ and separated by a distance of $0.4\,mm$ constitute an electric dipole. If the dipole is placed in a uniform electric field $\vec{E}$ of $10\,dyne/C$ making a $30^{\circ}$ angle with $\vec{E}$,the magnitude of torque acting on the dipole is: