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  4. 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 kgm -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 × 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 ×(10)-19 C) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-rwtjbdqjtbod8dql.jpg />

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Q. 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 $900\, kgm ^{-3}$ 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 $\left(e=1.6 \times(10)^{-19} C\right)$ Question

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
$qE=mg$ ..............(i)
$q=ne$
$V=Ed\Rightarrow E=\frac{V}{d}$
from equation (i)
$ne\frac{V}{d}=mg$
$n=\frac{ m g d }{e V}=900\times \frac{4 \pi }{3}\times \frac{8 \times 8 \times 8 \times 10^{- 21} \times 10 \times 0 . 01}{1 . 6 \times 10^{- 19} \times 200}$
$n=6.02\approx6$