An electric dipole with dipole moment $4 \times 10^{-14} \ C \cdot m$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^4 \ N/C$. The magnitude of the torque acting on the dipole is:

An electric dipole is placed on the $x$-axis with its center at the origin. The line $OP$ makes an angle $\theta$ with the $x$-axis. If the electric field at point $P$ is in the direction of the $y$-axis,what is the value of $\theta$?

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

Three charges are arranged on the vertices of a right-angled triangle as shown in the figure. The magnitude of the dipole moment of the combination in the unit of $C-cm$ is:

Two ideal electric dipoles $A$ and $B$ having dipole moments $p_{1}$ and $p_{2}$ respectively are placed on a plane with their centers at $O$ as shown in the figure. At point $C$ on the axis of dipole $A$,the resultant electric field makes an angle of $37^{\circ}$ with the axis. The ratio of the dipole moments of $A$ and $B$,$\frac{p_{1}}{p_{2}}$ is $....$ (take $\sin 37^{\circ}=\frac{3}{5}$)

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: