Q. Eight identical spherical drops, each carrying a charge 1 nC are at a potential of 900 V each. All these drops combine together to form a single large drop. Calculate the potential of this large drop. (Assume no wastage of any kind and take the capacitance of a sphere of radius r as proportional to r).

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Solution

Let small sphere volume =4/3pi.r^3
first we find volume of big sphere=8 x small sphere =8 x 4/3pi.r^3
R=2r
now
capacitance of small sphere=4pi. € r
where € is permitivity of medium

for big sphere capacitance=4pi. €.2r

It means
capacitance of big sphere=2 x capacitance of small sphere.

but we also know
C=Q/V and Q=CV
V=Q/C
now for big sphere
total charge in big sphere=8nC=8Cv
capacitance of big sphere=
8pi.€r=2CV=8Cv/2C
=4v=4×900=3600volt

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