Five charges, '$$q$$' each are placed at the comers of a regular pentagon of side '$$a$$' as shown in figure. First, charge from '$$A$$' is removed with other charges intact, then charge at '$$A$$' is replaced with an equal opposite charge. The ratio of magnitudes of electric fields at $$\mathrm{O}$$, without charge at $$A$$ and that with equal and opposite charge at $$A$$ is

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