Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of an $x-y$ coordinate system. Then:

An electric dipole with dipole moment $4 \times 10^{-9} \;C \,m$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^{4} \;N\,C ^{-1}$. Calculate the magnitude of the torque acting on the dipole.

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.

Point charges are fixed at the hour marks of a wall clock as shown. If the net dipole moment of the system is along the direction of the hour hand,then the time shown by the clock is:

$A$ 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.

$A$ system has two charges $q_{A} = 2.5 \times 10^{-7} \; C$ and $q_{B} = -2.5 \times 10^{-7} \; C$ located at points $A: (0, 0, -15 \; cm)$ and $B: (0, 0, +15 \; cm)$,respectively. What are the total charge and electric dipole moment of the system?