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 $(e)=1.6\times 10^{-19}C$ )

Answer 1

Answer: 6

Electric field between the discs after closing the switch
$E=\frac{V}{d}=\frac{200}{0.01}=2\times 10^{4}N/C$
When an oil drop stops and floats between the discs
$qE=mg$
$neE=mg$
$n=\frac{mg}{eE}=\frac{\rho \frac{4}{3}\pi r^{3}g}{eE}$
$n=900\times \frac{4\times 3.14\times {\left(8\times 10^{-7}\right)}^3\times 10}{3\times 1.6\times 10^{-19}\times 2\times 10^4}$
$n=\frac{3\times 4\times 3.14\times 2\times 8}{100}=6$
The number of electrons present in this oil drop is $n=6$