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Question

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

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Solution

Let us consider a bigger spherical drop of radius R. Then, the capacitance of this drop can be given as
CBig=4πϵ0R=12 μF
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
43πR3=8×43πr3
r=R2
We can say the capacitance of each small droplet formed will be Csmall=4πϵ0r=4πϵ0(R2)=CBig2=6 μF


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