Q. There are two concentric spheres of radius $a$ and $b$ respectively. If the space between them is filled with medium of resistivity $\rho$, then the resistance of the inter gap between the two spheres will be
A) $\frac{\rho}{4\pi(b + a)}$
B) $\frac{\rho}{4\pi}\left( \frac{1}{b} - \frac{1}{a} \right)$
C) $\frac{\rho}{4\pi}\left( \frac{1}{a^{2}} - \frac{1}{b^{2}} \right)$
D) $\frac{\rho}{4\pi}\left( \frac{1}{a} - \frac{1}{b} \right)$
Explanation
(d) Consider a concentric spherical shell of radius $x$ and thickness $dx$ as showing in figure. Its resistance, $dR$ is
$dR = \frac{\rho dx}{4\pi x^{2}}$
[image:3_image165.jpeg]
$\therefore$ Total resistance, $R = \frac{\rho}{4\pi}\int_{a}^{b}\ \frac{dx}{x^{2}} = \frac{\rho}{4\pi}\left\lbrack \frac{1}{a} - \frac{1}{b} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.