Two charges '$$-q$$' each are fixed, separated by distance '$$2 d$$'. A third charge '$$q$$' of mass '$$m$$' placed at the mid-point is displaced slightly by '$$x$$' $$(x< < d)$$ perpendicular to the line joining the two fixed charges as shown in Fig. The time period of oscillation of '$$q$$' will be

Two metal spheres, one of radius $$\frac{R}{2}$$ and the other of radius $$2 \mathrm{R}$$ respectively have the same surface charge density They are brought in contact and separated. The ratio of their new surface charge densities is

When $$10^{19}$$ electrons are removed from a neutral metal plate, the electric charge on it is

Two point charges $$20 \mu \mathrm{C}$$ and $$-10 \mu \mathrm{C}$$ are separated by a distance of $$1 \mathrm{~m}$$ in air. At what point on the line joining the two charges, the electric potential is zero.