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 $8\times {10}^{-7}$ m stops moving vertically and floats between the discs. The number of electrons present in this oil drop is ________.

Answer 1

Step 1: Given data:

Charged oil density, m = $900kg{m}^{-3}$

Voltage, v = 200 V

Oil drop radius, r = $8\times {10}^{-7}m$

Acceleration due to gravity , g= $10m{s}^{-2}$

Charge on an electron, e = $1.6\times {10}^{-19}C$

Step 2: Calculating the number of electrons present in this oil drop:

$qE=Mg$

$q=\frac{mg}{E}=\frac{900\times {\displaystyle \frac{4}{5}}\mathrm{\pi }{(8\times {10}^{-7})}^3\times 10}{{\displaystyle \frac{200}{0.01}}}$

$N=\frac{q}{e}$

$E=\frac{V}{d}$, where E= electric field

$N=\frac{mgd}{eV}$

$N=\frac{900\times 4\mathrm{\pi }\times 8^3\times {10}^{-21}\times 10\times 0.01}{200\times 1.6\times {10}^{-19}}$

$N=6$

The number of electrons present in this oil drop is 6.