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 8×10⁻⁷ 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)

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answer is 6.

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Detailed Solution

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