Question

A spherical drop of capacitance $12\mu F$ is broken into eight drops of equal radius. Then, what is the capacitance of each small drop in $\mu F$?

Answer 1

Let us consider a bigger spherical drop of radius R. Then, the capacitance of this drop can be given as
$C_{Big}=4\pi {ϵ}_{0}R=12\mu F$
Now , as this drop is broken into 8 equal size droplets, it means, the volume of the drop will remain conserved . If $r$ is the radius of small droplets formed then, we can say
$\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3$
$⟹r=\frac{R}{2}$
$\therefore$ We can say the capacitance of each small droplet formed will be $C_{small}=4\pi {ϵ}_{0}r=4\pi {ϵ}_0\left(\frac{R}{2}\right)=\frac{C_{Big}}{2}=6\mu F$