Connecting Spheres Consider two hollow spherical conducting shells, Conductor A with radius 3R and Conductor B with radius R, which are separated by a very large distance d ?R. The shells are thin enough that you may use the same radius (3R or R) as both the inner and outer radius in your calculations, but they have enough thickness that we can consider them to have distinct inner and outer charge densities. Initially, each conductor has a charge +Q and they are not connected electrically. A wire is then connected between the two conductor surfaces, allowing charge to possibly move between them.

INITIAL R A B 3R VB. i +Q +Q VA. i FINAL A B VB.J VA.fa) Calculate and rank the surface charge density of each of the conductors, before (0 A,i, OB,i) and after (0A,S, OB,f) the wire is connected, on both the inside and outside surfaces. (You should have 8 terms, one per surface (inner and outer) per shell (A and B) per case (before and after).) b) Now calculate and rank the electric potential at each surface of each of the conductors, before (VA,i, VB,i) and after (VA,S, VB,f ), in the same manner as in part (a). Argue your choice of ranking. c) Repeat parts (a) and (b) in the situation where there is also a point charge -Q fixed in place at the center of shell A and another point charge -Q fixed in place at the center of shell B. d) Recall that we assumed the distance, d, between two conducting shells is very large com- pared to the radius R (d > R). Now consider that the distance, d, is comparable to the radius R (d ~ R)? How would this close distance between shells affect your answers above? You don't have to provide your answers rigorously for this question. As an example, you might say that there would be no need to change the solutions. Or the surface charge density on the outside surface of Conductor A must be altered and so on. Support your