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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 ($e$) $=1.6 \times 10^{-19} C$ )
$6$
$7$
$8$
$9$
Solution
$E =\frac{ V }{ d }=\frac{200}{0.01}=2 \times 10^4 V / m$
When terminal velocity is achieved
$qE = mg$
$\Rightarrow n \times 1.6 \times 10^{-19} \times 2 \times 10^4=\frac{4 \pi}{3}\left(8 \times 10^{-7}\right)^3 \times 900 \times 10$
$\Rightarrow n \approx 60$
