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

Answer 1

Answer: 6

$qE=mg$ ..............(i)
$q=ne$
$V=Ed\Rightarrow E=\frac{V}{d}$
from equation (i)
$ne\frac{V}{d}=mg$
$n=\frac{mgd}{eV}=900\times \frac{4\pi }{3}\times \frac{8\times 8\times 8\times 10^{-21}\times 10\times 0.01}{1.6\times 10^{-19}\times 200}$
$n=6.02\approx 6$