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64 identical water dorps coalesce to for...

64 identical water dorps coalesce to form a larger drop. If the nature and amount of charge be the same for all the drops, calculate the potential, capacitance and stored energy of the larger drop.

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Let the radii of small and large drops be r and R respectively and the charge of each small drop be Q. According to the question,
`(4)/(3) piR^3 = 64xx(4)/(3)pir^3 " or, "R = 4r`
Potential of small drop, `V= (Q)/(r )" or, "Q= Vr`
Potential of large drop, `V' =(64Q)/(R )=(64Vr)/(4r)=16V`
i.e., the potential of large drop will be 16 times the potential of small drop.
As the radius of large drop is 4r, its capacitance, C =4r.
The energy stored in the large drop,
`E = (1)/(2)CV'^2= (1)/(2)xx4rxx(16V)^2= 512rV^2`.
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