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