Q. The earth has Volume $'V'$ and surface area $'A'$ then capacitance would be
A) $4\pi \in_{0}\frac{A}{V}$
B) $4\pi \in_{0}\frac{V}{A}$
C) $12\pi \in_{0}\frac{V}{A}$
D) $12\pi \in_{0}\frac{A}{V}$
Explanation
(c) For spherical conductor
$C = 4\pi\varepsilon_{0}R$
$\because V = \frac{4}{3}\pi R^{3}\ \&\ A = 4\pi R^{2}$
$\because R = \frac{3V}{A}$
$\therefore C = 12\pi\varepsilon_{0}\frac{V}{A}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.