Question

Space between two concentric conducting spheres of radii $a$ and $b(b>a)$ is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be :

• A. $\frac{\rho }{4\pi }\left(\frac{1}{a}-\frac{1}{b}\right)$
• B. $\frac{\rho }{2\pi }\left(\frac{1}{a}-\frac{1}{b}\right)$
• C. $\frac{\rho }{2\pi }\left(\frac{1}{a}+\frac{1}{b}\right)$
• D. $\frac{\rho }{4\pi }\left(\frac{1}{a}+\frac{1}{b}\right)$

Answer 1

Answer: (A)

$dR=\rho .\frac{dx}{4\pi x^2}$
$\int dR=\rho .{\int }_a^b\frac{dx}{4\pi x^2}$
$R=\frac{\rho }{4\pi }{\left[-\frac{1}{x}\right]}_a^b$
$R=\frac{\rho }{4\pi }\left(\frac{1}{a}-\frac{1}{b}\right)$