Q. 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) $16q,\ 64C$
Explanation
(c) 64 small spheres have formed have formed a single large spheres of radius $R$
$\therefore\frac{4}{3}\pi R^{3} = 64 \times \frac{4}{3}\pi r^{3} \Rightarrow R = 4r$
$Q_{total} = 64q$
As $C^{'} = \frac{Q}{V}$ and $V = \frac{1}{4\pi\varepsilon_{0}}\frac{Q}{R};$
$C^{'} = 4\pi\varepsilon_{0}R$
$C^{'} = \left( 4\pi\varepsilon_{0} \right).\ 4r \Rightarrow C^{'} = 4C$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.