Q. A solid conducting sphere of radius $R_{1}$ is surrounded by another concentric hollow conducting sphere of radius $R_{2}.$ The capacitance of this assembly is proportional to
A) $\frac{R_{2} - R_{1}}{R_{1}R_{2}}$
B) $\frac{R_{2} + R_{1}}{R_{1}R_{2}}$
C) $\frac{R_{1}R_{2}}{R_{1} + R_{2}}$
D) $\frac{R_{1}R_{2}}{R_{2} - R_{1}}$
Explanation
(d) Capacitance of the given assembly
$C = 4\pi\varepsilon_{0}\left( \frac{R_{1}R_{2}}{R_{2} - R_{1}} \right) \Rightarrow C \propto \frac{R_{1}R_{2}}{(R_{2} - R_{1})}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.