Two short dipoles $P \hat{\mathrm{k}}$ and $\frac{P}{2} \hat{\mathrm{k}}$ are located at $(0, 0, 0)$ and $(1 \mathrm{m}, 0, 2 \mathrm{m})$, respectively. The resultant electric field due to the two dipoles at the point $(1 \mathrm{m}, 0, 0)$ is

Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point $O$ and perpendicular to the plane of the figure as a function of distance $x$ from point $O$ is (assume $x>>a$)

An electric dipole is placed in a uniform electric field $\overrightarrow{E}$ of magnitude $40 \mathrm{N} {\mathrm{C}}^{-1}$. The graph below shows the magnitude of the torque on the dipole versus the angle $\mathrm{\theta }$ between the field $\overrightarrow{E}$ and the dipole moment $\overrightarrow{p}$. The magnitude of dipole moment $\overrightarrow{p}$ is equal to