A spherical drop of capacitance 12μF 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=12μF 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=6μF