A cube of side 1 cm contains 100 molecules each having an induced dipole moment of $0.2 \times 10^{-6} \mathrm{C}-\mathrm{m}$ in an external electric field of $4 \mathrm{NC}^{-1}$. The electric susceptibility of the materials is ................ $\mathrm{~C^2N}^{-1} \mathrm{~m}^{-2}$

A positively charged glass rod is brought near uncharged metal sphere, which is mounted on an insulated stand. If the glass rod is removed, the net charge on the metal sphere is

In the situation shown in the diagram, magnitude, if $$q < < |Q|$$ and $$r >>>a$$. The net force on the free charge $$-q$$ and net torque on it about $$O$$ at the instant shown are respectively.

($$p=2 a Q$$ is the dipole moment)

A uniform electric field vector $$\mathbf{E}$$ exists along horizontal direction as shown. The electric potential at $$A$$ is $$V_A$$. A small point charge $$q$$ is slowly taken from $$A$$ to $$B$$ along the curved path as shown. The potential energy of the charge when it is at point $$B$$ is