Question 251: Electrostats & Capacitance

Question

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 $$ 	imes $$ 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 $$ 	imes $$ 10–19 C)

Accepted Answer

$$qE = Mg $$
$$\Rightarrow q = {{mg} \over E} = \left( {{{mg} \over {V/d}}} ight)$$
$$ = {{900 	imes {4 \over 5}\pi (8 	imes {{10}^{ - 7}}) 	imes 10} \over {{{200} \over {0.01}}}}$$
$$N = {q \over e} = {{900 	imes 4\pi  	imes {8^3} 	imes {{10}^{ - 21}} 	imes 10 	imes 0.01} \over {200 	imes 1.6 	imes {{10}^{ - 19}}}}$$
N = 6

Electrostats & Capacitance

Choose the correct answer: