Two coaxial dipoles of dipole moments $p_1$ and $p_2$ are separated by a distance $r.$ The magnitude of electric force on $p_1$ due to $p_2$ is $\left(k=\frac{1}{4\mathrm{\pi }{\epsilon }_0}\right)$

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

A wheel having mass $m$ has charges $+q$ and $-q$ on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of a uniform vertical electric field $E.$ The value of $E$ is