Hollow metal sphere # 1 has inner radius a, outer radius 3a, and net charge Q > 0. Hollow metal sphere # 2 has inner radius 3a, outer radius 6a, and net charge −2Q. At the center of the cavity in sphere # 1 is a point charge 2Q. The two spheres are very far apart.
(a) Find the charge on each surface (inner, outer) of each sphere.
(b) Find the voltage between a point on the outer surface of sphere # 1 and a point on the outer surface of sphere # 2.
(c) A very long, fine wire is used to connect the outer surfaces of the two spheres, allowing electrons to flow between them. After the charge distribution reaches equilibrium, what are the charges on each surface of each sphere? Assume the charge on the surfaces of the wire is negligible because the radius of the wire is very small compared to the radii of the spheres. Hint: Consider the voltages between different points on the spheres.