Question

How many times, the potential of big drop in comparison to small drops which is made of $8$ droplets will be, if all the droplets are identical?

• A. 2 times
• B. 4 times
• C. 3 times
• D. 8 times

Answer 1

Answer: (B)

Volume of bigger drop $=8\times$ volume of small drops
$\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3$
$R=2r$
Potential on small drop $V_1=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$
Potential on bigger drop
$V_2=\frac{1}{4\pi {\epsilon }_0}\frac{8q}{R}$
$=\frac{1}{4\pi {\epsilon }_0}\frac{8q}{2r}$
$=4\left(\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}\right)$
$=4V_1$
So, potential on the bigger is four times to that potential on small.