Question

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

• A. 800 V
• B. 1600 V
• C. 3200 V
• D. 400 V

Answer 1

The correct option is C 3200 V

From the figure, $F_e$ and $F_g$ represents electric and gravitational forces respectively.
We can observe that,

$V\propto \frac{m}{q}$

and in turn $m\propto r^3$
given V = 400V is initial voltage and let $V_1$
substituting these values in the respective equations we get

$\frac{V_1}{V}=\frac{(2r{)}^{3}q}{r^3\left(q\right)}$

solving the above eqaution will give us
$V_1=8\times V=3200$ V

So, the answer is option (C).