Question

$64$ 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

• A. $64q,C$
• B. $16q,4C$
• C. $64q,4C$
• D. $16q,64C$

Answer 1

Answer: (C)

$64$ drops have formed a single drop of radius $R$.
Volume of big drop = Volume of smalls drop.
$\therefore \frac{4}{3}\pi R^3=64\times \frac{4}{3}\pi r^3$
$\Rightarrow R=4r$
So, the total current is
$Q_{\text{total}}=64q$
As $C^{\prime }=\frac{Q}{V}$
and $V=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{R};$
$C^{\prime }=4\pi {\epsilon }_{0}R$
$C^{\prime }=\left(4\pi {\epsilon }_0\right)4r$
$\Rightarrow C^{\prime }=4C.$