Question

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. $\frac{\rho}{4 \pi}\left(\frac{1}{a}-\frac{1}{b}\right)$

Answer 1

Answer: (D)

Consider a concentric spherical shell of radius $x$ and thickness $d x$ as showing in figure. Its resistance, $d R$ is $d R=\frac{\rho d x}{4 \pi x^{2}}$

$\therefore $ Total resistance, $R=\frac{\rho}{4 \pi} \frac{ d x}{x}=\frac{\rho}{4 \pi}\left(\frac{1}{a}-\frac{a}{b}\right)$