Chapter 25, Problem 25.60P

CALC The region between two concentric conducting spheres with radii a and b is filled with a conducting material with resistivity ρ. (a) Show that the resistance between the spheres is given by

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

(b) Derive an expression for the current density as a function of radius, in terms of the potential difference V_ab between the spheres, (c) Show that the result in part (a) reduces to Eq. (25.10) when the separation L = b = a between the spheres is small.