Question

In Millikan’s oil drop experiment, an oil drop having charge is held stationary with an external p.d of 400 V. If the radius of the drop is doubled without any change in charge, the p.d required to keep the drop stationary is

• A. 800 V
• B. 1600 V
• C. 3200 V
• D. 200 V

Answer 1

The correct option is C 3200 V

Let the distance between plates be $d$
Radius of drop $=r$
and Density of the fluid $=D$
From 1st condition according to question,
$\frac{4}{3}\pi r^{3}Dg=q\left(\frac{400}{d}\right)$--------------------- (I)

According to 2nd condition, let Voltage required by $V_0$,
$\frac{4}{3}\pi {\left(2r\right)}^{3}Dg=q\left(\frac{V_0}{d}\right)$
$\Rightarrow 8\left(\frac{4}{3}{r}^{3}Dg\right)=\frac{q}{d}\left(V_0\right)$ ----------------(II)
From (I) and (II),
$V_0=(8\times 400)volts$
$\Rightarrow V_0=3200volts$

So, the answer is option (C).