A metal sphere with radius $r_a$ is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius $r_b$ . There is charge $+q$ on the inner sphere and charge $-q$ on the outer spherical shell. Use $E_{r} = - \partial V / \partial r = (- \partial / \partial r) (1 / (4 π ϵ_{0}) q / r) = [1 / (4 π ϵ_{0})] (q / r^{2})$ and the result from part (a) to show that the electric field at any point between the spheres has magnitude $E (r) = [V_{a} b / (1 / r_{a} - 1 / r_{b})] (1 / r^{2})$ . Note: Part (a) asked to calculate the potential $V(r)$ for (i) $r < r_a$ ; (ii) $r_a < r < r_b$ ; (iii) $r > r_b$ . (Hint: The net potential is the sum of the potentials due to the individual spheres.) Take $V$ to be zero when $r$ is infinite..

25. Electric Potential

Equipotential Surfaces