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:

$A$ and $B$ are two points on the axis and the perpendicular bisector respectively of an electric dipole. $A$ and $B$ are far away from the dipole and at equal distance from it. The electric fields at $A$ and $B$ are $\vec{E}_A$ and $\vec{E}_B$.

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

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 $.....$

If the electric field at a distance $x$ on the axis of an electric dipole is equal to the electric field at a distance $y$ on its equatorial line,what is the ratio $x : y$?

Electric charges $q, q, -2q$ are placed at the corners of an equilateral triangle $ABC$ of side $l$. The magnitude of the electric dipole moment of the system is