Two charged particles each of mass $9.8 \text{ g}$ and charges $+20 \mu\text{C}$ and $-20 \mu\text{C}$ are attached to the two ends of a massless and rigid uniform non-conducting rod of length $50 \text{ cm}$. This arrangement is held in a uniform electric field of $12.1 \text{ N/C}$,such that the rod makes a very small angle with the field direction. If the rod is set free,the minimum time needed for the rod to become parallel to the direction of the electric field is ................ seconds.

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. . . . . .

When does the torque acting on an electric dipole in a uniform electric field become zero?

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.

An electric dipole is placed at an angle of $30^{\circ}$ in a non-uniform electric field. The electric dipole will experience:

The electric potential at a point due to an electric dipole is maximum and minimum when the angles between the axis of the dipole and the line joining the point to the center of the dipole are respectively: