Two electric dipoles of dipole moments $1.2 \times 10^{-30} \, C \cdot m$ and $2.4 \times 10^{-30} \, C \cdot m$ are placed in two different uniform electric fields of strengths $5 \times 10^{4} \, N \cdot C^{-1}$ and $15 \times 10^{4} \, N \cdot C^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of $x$ is $.....$

An electric dipole of moment $\vec{p}$ is kept in a uniform electric field $\vec{E}$. The angle between $\vec{p}$ and $\vec{E}$ is $30^\circ$. Calculate the work done by the field when the angle is increased to $60^\circ$.

An electric dipole of moment $\vec{P}$ is placed in a uniform electric field $\vec{E}$ such that $\vec{P}$ points along $\vec{E}$. If the dipole is slightly rotated about an axis perpendicular to the plane containing $\vec{E}$ and $\vec{P}$ and passing through the centre of the dipole, the dipole executes simple harmonic motion. Consider $I$ to be the moment of inertia of the dipole about the axis of rotation. What is the time period of such oscillation?

$A$ dipole having a dipole moment $p = 4 \, C-m$ is placed at the origin along the $x$-axis. $A$ point charge $q = 8 \, \mu C$ is fixed at $(4, 0, 0)$. Now,the dipole is rotated by an angle of $\frac{\pi}{2}$. Find the work done (in $mJ$) in rotating the dipole.

If $E_{a}$ and $E_{q}$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance $r$ from the centre of the dipole,then

An electric dipole is kept on the axis of a uniformly charged ring at a distance of $R/\sqrt{2}$ from the center of the ring. The direction of the dipole moment is along the axis. The dipole moment is $P$,the charge of the ring is $Q$,and the radius of the ring is $R$. The force on the dipole is nearly: