Question

In Millikan's oil drop experiment, an oil drop is held stationary by a potential difference of $400$ V. If another drop of double the radius, but carrying the same charge, is to be held stationary, find the potential difference required ?

Answer 1

Given,

$V=400V$

$r^{\prime }=2r$

From the free body diagram,

$qE=mg$

$q\frac{V}{d}=\frac{4}{3}\pi r^3\rho g$

where, $V=$ potential difference

$\rho =density$

From the abvove equation,

$V\propto r^3$

$\frac{V^{\prime }}{V}=\frac{r^{\prime 3}}{r^3}=\frac{8r^3}{r^3}=8$

$V^{\prime }=8V=8\times 400$

$V^{\prime }=3200V$