Question

Two large circular discs separated by a distance of $0.01m$ are connected to a battery via a switch as shown in the figure. Charged oil drops of density $900kg m^{- 3}$ 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 $200V$ 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 $\left(e\right)=1.6\times \left(10\right)^{- 19}C$ )

Answer 1

$ E =\frac{ V }{ d }=\frac{200}{0.01}=2 \times 10^{4} V / m $
When terminal velocity is achieved
$ q E=m g \Rightarrow n \times 1.6 \times 10^{-19} \times 2 \times 10^{4}=\frac{4 \pi}{3}\left(8 \times 10^{-7}\right)^{3} \times 900 \times 10 \Rightarrow n \approx 6 $