Question

64 identical spheres of charge q and capacitance C each are combined to form a large sphere. 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 small's drops.
$\therefore \frac{4}{3}\pi R^3=64\times \frac{4}{3}\pi r^3$
$\Rightarrow R=4r$
So, the total current is
$Q_{total}=64q$
As $C^{\prime }=\frac{Q}{V}andV=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{R};C^{\prime }=4\pi {\epsilon }_{0}R$
$C^{\prime }=\left(4\pi {\epsilon }_0\right)4r\Rightarrow C^{\prime }=4c$.