First slide

Electrostatic potential

Question

An oil drop having charge 2e is kept stationary between two parallel horizontal plates 2.0 cm apart when a potential difference of 12000 volts is applied between them. If the density of oil is 900 kg/m³, the radius of the drop will be

Moderate

A

$2 .0 \times 10^{- 6} m$
B

$1 .7 \times 10^{- 6} m$
C

$1 .4 \times 10^{- 6} m$
D

$1 .1 \times 10^{- 6} m$

Solution

In equilibrium $QE = mg \Rightarrow Q \cdot \frac{V}{d} = mg = (\frac{4}{3} {πr}^{3} ρ) g$
$\Rightarrow 2 \times 1 .6 \times 10^{- 19} \times \frac{12000}{2 \times 10^{- 2}} = \frac{4}{3} {πr}^{3} \times 900 \times 10$
$\Rightarrow r = 1 .7 \times 10^{- 6} m$

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