A tiny spherical oil drop of mass 8 mg is kept suspended by applying a potential difference of 100 V between two metallic plates kept separated by a distance 1 cm. The number of electrons on the oil drop are: (Take \( g = 10\,\mathrm{m\,s^{-2}} \))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 5\times10^{10} \)
The drop stays suspended when the upward electric force balances its weight, \( qE = mg \), where the field between the plates is \( E = V/d \). The charge is then a whole number n of electron charges, \( q = ne \).
Conversions: \( m = 8\,\mathrm{mg} = 8\times10^{-6}\,\mathrm{kg} \) and \( d = 1\,\mathrm{cm} = 10^{-2}\,\mathrm{m} \).
\( \displaystyle E = \frac{V}{d} = \frac{100}{10^{-2}} = 10^{4}\,\mathrm{V/m} \)
\( \displaystyle q = \frac{mg}{E} = \frac{8\times10^{-6}\times10}{10^{4}}\,\mathrm{C} = 8\times10^{-9}\,\mathrm{C} \)
\( \displaystyle n = \frac{q}{e} = \frac{8\times10^{-9}}{1.6\times10^{-19}} = 5\times10^{10} \)