Question

Hi Friends please solve this 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 900kg 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​

Answer 1

$Answer \Rarr \: 6 \: electrons$

Step-by-step explanation:

As the droplet gains Terminal velocity it's velocity becomes constant as drag force equals gravitational force in opposite directions.

But when we apply voltage Electric field is generated from upwards to downward but the drop experience force in upward direction due to negative charge present on it.

After some time velocity of drop become zero due to presence of force opposite to velocity than mg will act downward and electric force act upward on droplet

It is given in question that drop start floating after applying voltage this means that electric force equals gravitational force

now we have to find number of electrons in droplet

$QE=gravitational \: force$

$QE=\rho \: \times \frac{4\pi {r}^{3} }{3}$

Let number of electrons be X

$1.6 \times {10}^{ - 19} \times x \times \frac{v}{d} = \rho \times \frac{4}{3} \times \pi \times {r}^{3}$

put values of density v,d and r

$x = 6.049$

as number of electrons can only be a integer

than x will be 6

ADDITIONAL INFORMATION

QUESTION :- IIT2020 (PAPER2)

THE VALUE OF DRAG FORCE IS :-

$6\pi\eta \: rv$

Answer 2

$Answer \Rarr \: 6 \: electrons$

Step-by-step explanation:

As the droplet gains Terminal velocity it's velocity becomes constant as drag force equals gravitational force in opposite directions.

But when we apply voltage Electric field is generated from upwards to downward but the drop experience force in upward direction due to negative charge present on it.

After some time velocity of drop become zero due to presence of force opposite to velocity than mg will act downward and electric force act upward on droplet

It is given in question that drop start floating after applying