Question

An oil drop of $n$ excess electrons is held stationary under a constant electric field $E$ in Millikan?s oil drop experiment. The density of oil is $\rho$ . The radius of the drop is

• A. $\left[\frac{3ne E}{2 \pi \rho g}\right]^{1/2}$
• B. $\left[\frac{3n\rho g}{2 \pi eE}\right]^{1/2}$
• C. $\left[\frac{3nEe}{4 \pi \rho g}\right]^{1/3}$
• D. $\left[\frac{3n\rho g}{4 \pi eE}\right]^{1/3}$

Answer 1

Answer: (C)

$\left[\frac{3nEe}{4 \pi \rho g}\right]^{1/3}$

Answer 2

In Millikan?s oil drop experiment, the charged oil drop remains suspended (in equilibrium) when downward weight of drop is balanced by upward electrostatic force and charge on drop $q = ne$, i.e.
$qE = mg$
$\Rightarrow neE = mg$
If $r$ is radius of oil drop, then mass $m = \frac{4}{3} \pi r^3 \rho$
$neE = \frac{4}{3} \pi r^3 \rho g$
$r = \left[\frac{3neE}{4\pi \rho g}\right]^{1/3}$