A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$, and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n q}{6 \epsilon_{0}}$ (in SI units). The value of $n$ is _______.

Two point charges $$-$$Q and +Q/$$\sqrt 3 $$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.



The value of R is __________ meter.

Two point charges $$-$$Q and +Q/$$\sqrt 3 $$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.



The value of b is __________ meter.

Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density 900 kg m⁻³ are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of 200 V across the discs. As a result, an oil drop of radius 8 $$ \times $$ 10⁻⁷ m stops moving vertically and floats between the discs. The number of electrons present in this oil drop is ________.
(neglect the buoyancy force, take acceleration due to gravity = 10 ms⁻² and charge on an electron (e) = 1.6 $$ \times $$ 10^–19 C)