An electric dipole with dipole moment $p$ is placed with its axis at $30^{\circ}$ to a uniform electric field. The work done in rotating the dipole to a position where its axis is perpendicular to the field is

Two tiny electric dipoles of dipole moments $P_1$ and $P_2$ are placed at a distance $r$ coaxially. Find the magnitude of the electrostatic force between them.

An electric dipole of moment $\overrightarrow{p} = (-\hat{i} - 3\hat{j} + 2\hat{k}) \times 10^{-29} \; C \cdot m$ is at the origin $(0, 0, 0)$. The electric field due to this dipole at $\overrightarrow{r} = \hat{i} + 3\hat{j} + 5\hat{k}$ (note that $\overrightarrow{r} \cdot \overrightarrow{p} = 0$) is parallel to

Three identical dipoles are arranged as shown below. What will be the net electric field at $M$?

The electric field due to a short electric dipole at a distance $r$ on the axial line from its mid-point is $x$ times the electric field at a distance $2r$ on the equatorial line from the mid-point of the dipole. Then,the value of $x$ is

An electric dipole moment $\vec{p} = (2.0\hat{i} + 3.0\hat{j}) \times 10^{-6} \text{ C m}$ is placed in a uniform electric field $\vec{E} = (3.0\hat{i} + 2.0\hat{k}) \times 10^{5} \text{ N C}^{-1}$. Which of the following statements is correct?