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 $=10m{s}^{-2}$ and charge on an electron $\left(e\right)=1.6\times {\left(10\right)}^{-19}C$ )

Answer 1

Answer: 6

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