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Q.
$64$ identical spheres of charge $q$ and capacitance $C$ each are combined to form a large sphere is The charge and capacitance of the large sphere is
WBJEEWBJEE 2008Electrostatic Potential and Capacitance
Solution:
$64$ drops have formed a single drop of radius $R$.
Volume of big drop = Volume of smalls drop.
$\therefore \frac{4}{3} \pi R^{3}=64 \times \frac{4}{3} \pi r^{3}$
$\Rightarrow R=4 r$
So, the total current is
$Q_{\text {total}}=64 q$
As $C'=\frac{Q}{V}$
and $V=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{R} ;$
$C'=4 \pi \varepsilon_{0} R$
$C'=\left(4 \pi \varepsilon_{0}\right) 4 r$
$\Rightarrow C'=4 C .$