Walker, Halliday & Resnick — Electric Potential: Problem 36

36 Sphere 1 with radius \(R_1\) has positive charge \(q\). Sphere 2 with radius \(3.00R_1\) is far from sphere 1 and initially uncharged. After the separated spheres are connected with a wire thin enough to retain only negligible charge, (a) is potential \(V_1\) of sphere 1 greater than, less than, or equal to potential \(V_2\) of sphere 2? What fraction of \(q\) ends up on (b) sphere 1 and (c) sphere 2? (d) What is the ratio \(\sigma_1/\sigma_2\) of the surface charge densities of the spheres?